Deck 2: Polynomial and Rational Functions

Question 1

Solve the inequality and graph the solution on the real number line.
$( x - 7 ) ^ { 2 } \geq 1$

A) $( - \infty , - 6 ] \cup [ - 8 , \infty )$
B) $( - \infty , 6 ] \cup [ 8 , \infty )$
C) $( - \infty , 8 ] \cup [ 6 , \infty )$
D) $( - \infty , 8 ] \cup [ 6 , \infty )$
E) $( - \infty , 6 ] \cup [ 8 , \infty )$

Answer 1

$( - \infty , 6 ] \cup [ 8 , \infty )$

Question 2

Solve the inequality and graph the solution on the real number line.
$x ^ { 2 } + 5 x + 13 > 0$

A) $x \geq - 13$
B) $x \leq 13$
C) $x > 5$
D) $x < - 5$
E)All real numbers

Answer 2

All real numbers

Question 3

Solve the inequality and write the solution set in interval notation.
$5 x ^ { 3 } - 20 x ^ { 2 } > 0$

A) $( 4 , \infty )$
B) $( - 4 , - \infty )$
C) $( - 4 , \infty )$
D) $( 4 , - \infty )$
E) $( - \infty , 5 )$

Answer 3

$( 4 , \infty )$

Question 4

Solve the inequality and write the solution set in interval notation.
$x ^ { 3 } - 36 x \geq 0$

A) $[ - 6,0 ] \cup [ 6 , \infty ]$
B) $[ - 6,0 ] \cup [ 6 , \infty )$
C) $[ - 36,0 ] \cap [ 6 , \infty ]$
D) $[ - 36,0 ] \cup [ - 6 , \infty )$
E) $[ - 6,0 ] \cap [ 6 , \infty )$

Question 5

Solve the inequality and graph the solution on the real number line.
$x ^ { 2 } - 10 x - 24 > 0$

A) $( - \infty , - 2 ) \cup ( 12 , \infty )$
B) $( - \infty , - 2 ) \cap ( - 12 , \infty )$
C) $( - \infty , - 2 ) \cup ( - \infty , - 12 , )$
D) $( \infty , - 2 ) \cup [ 12 , \infty )$
E) $( - \infty , 2 ] \cup ( 12 , \infty )$

Question 6

Solve the inequality and graph the solution on the real number line.
$x ^ { 2 } - 10 x + 8 < 19$

A) $( - 1,11 )$
B) $( - 1 , - 11 )$
C) $( 1 , - 11 )$
D) $( - 1 , - 11 )$
E) $( - 1,11 )$

Question 7

Solve the inequality and graph the solution on the real number line.
$x ^ { 2 } < 4$

A) $[ - 2,2 ]$
B) $[ - 2,2 ]$
C) $( - 2,2 )$
D) $( - 2,2 )$
E) $( - 2,2 )$

Question 8

Solve the inequality and graph the solution on the real number line.
$x ^ { 3 } - 3 x ^ { 2 } - x > - 3$

A) $( - 1,1 ) \cup ( 3 , \infty )$
B) $( - 1,1 ) \cup ( - 3 , \infty )$
C) $( - 1,1 ) \cup ( 3 , \infty )$
D) $( - 1,1 ) \cup ( - 3 , - \infty )$
E) $( - 1,1 ) \cup ( - 3 , \infty )$

Question 9

Solve the inequality and graph the solution on the real number line
$x ^ { 3 } + 3 x ^ { 2 } - 9 x - 27 \leq 0$

A) $( - \infty , 3 ]$
B) $( - \infty , 3 )$
C) $( - \infty , 3 ]$
D) $( - \infty , - 3 ]$
E) $( - \infty , - 3 )$

Question 10

Determine whether the value of $x = - 6$ is a solution of the inequality. $x ^ { 2 } - x - 14 \geq 0$

Question 11

Determine whether the value of $x = - 1$ is a solution of the inequality. $\frac { 3 x ^ { 2 } } { x ^ { 2 } + 4 } < 1$

Question 12

Solve the inequality and graph the solution on the real number line.
$x ^ { 2 } + 3 x > 4$

A) $( - \infty , - 4 ) \cup ( 1 , \infty )$
B) $( - \infty , - 4 ) \cup ( - 1 , \infty )$
C) $( - \infty , - 4 ) \cup ( 1 , \infty )$
D) $( - \infty , - 4 ) \cup ( - 1 , \infty )$
E) $( - \infty , - 4 ) \cup ( 1 , - \infty )$

Question 13

Determine whether the value of $x = \frac { 2 } { 7 }$ is a solution of the inequality. $x ^ { 2 } - 2 < 0$

Question 14

Solve the inequality and write the solution set in interval notation.
$6 x ^ { 2 } - 10 x < 0$

A) $( - \infty , 0 ) ] \cup [$ $\frac { 5 } { 3 }$ $, \infty )$
B) $\varnothing$
C) $( - \infty , 0 )$ $\frac { 5 } { 3 }$ $, \infty )$
D) $( \infty , 0 ) \cup [ -$ $\frac { 5 } { 3 }$ $, \infty )$
E) $( 0 ,$ $\frac { 5 } { 3 }$ )

Question 15

Solve the inequality and graph the solution on the real number line.
$x ^ { 2 } + x < 12$

A) $( - 4,3 )$
B) $( - 4,3 )$
C) $( 4,3 )$
D) $( - 4 , - 3 )$
E) $( - 4 , - 3 )$

Question 16

Find the key numbers of the expression.
$\frac { 1 } { x - 7 } + 1$

A)-6, 7
B)6, 7, 1
C)-6, -7
D)6, 7
E)6, -7

Question 17

Solve the inequality and graph the solution on the real number line.
$9 x ^ { 2 } - 6 x + 1 \leq 0$

A) $x = 3$
B) $x = \frac { 1 } { 3 }$
C) $x = \frac { 1 } { 9 }$
D) $x = - \frac { 1 } { 3 }$
E) $x = - 3$

Question 18

Solve the inequality and graph the solution on the real number line.
$x ^ { 2 } > 2 x + 48$

A) $( - \infty , - 6 ) \cup ( 8 , \infty )$
B) $( - \infty , 6 ) \cup ( 8 , \infty )$
C) $( - \infty , - 6 ) \cup ( - 8 , - \infty )$
D) $( - \infty , - 6 ) \cup ( - 8 , \infty )$
E) $( - \infty , 6 ) \cup ( 8 , \infty )$

Question 19

Find the key numbers of the expression.
$16 x ^ { 3 } - 49 x ^ { 2 }$

A)0, $\frac { 16 } { 49 }$
B)0, 49
C)0, 51
D)0, -49
E)0, $\frac { 49 } { 16 }$

Question 20

Solve the inequality and graph the solution on the real number line
$x ^ { 2 } \leq 9$

A) $( - 3,3 )$
B) $[ - 3,3 ]$
C) $[ - 3,3 ]$
D) $[ 3 , - 3 ]$
E) $( - 3,3 )$

Question 21

Solve the inequality and graph the solution on the real number line. $\frac { 4 x - 1 } { x } > 0$

A) $( - \infty , 0 ) \cup \left( \frac { 1 } { 4 } , \infty \right)$
B) $( - \infty , 0 ) \cup \left( - \frac { 1 } { 4 } , \infty \right)$
C) $( - \infty , 0 ) \cap \left( - \frac { 1 } { 4 } , \frac { 1 } { 4 } \right)$
D) $( - \infty , 0 ) \cap \left( \frac { 1 } { 4 } , \infty \right)$
E) $( - \infty , 0 ) \cap \left( - \frac { 1 } { 4 } , \infty \right)$

Question 22

Use a graphing utility to graph the equation.Use the graph to approximate the values of x that satisfy the following inequality.
Equation: $y = \frac { 7 x } { x ^ { 2 } + 6 }$
Inequality: $y \geq 1$

A) $1 \leq x \leq 6$
B) $1 \leq x < 6$
C) $1 < x < 6$
D) $1 < x \leq 6$
E) $1 < x \leq 6$

Question 23

Solve the inequality and graph the solution on the real number line.
$\frac { x ^ { 2 } + x - 12 } { x } \geq 0$

A) $[ - 4,0 ) \cap [ 3 , \infty )$
B) $[ 4,0 ) \cup [ 3 , \infty )$
C) $[ 4,0 ) \cup [ - 3 , \infty )$
D) $[ - 4,0 ) \cap [ - 3 , \infty )$
E) $[ - 4,0 ) \cup [ 3 , \infty )$

Question 24

Find the domain of x in the expression.
$\sqrt { x ^ { 2 } - 7 x + 12 }$

A) $( - \infty , 3 ] \cup [ 4 , \infty )$
B) $( - \infty , 3 ] \cap [ 4 , \infty )$
C) $( \infty , - 3 ] \cup [ 4 , \infty )$
D) $( \infty , 3 ] \cap [ 4 , \infty )$
E) $( \infty , - 3 ] \cap [ 4 , \infty )$

Question 25

Use a graphing utility to graph the equation.Use the graph to approximate the values of x that satisfy each inequality.
Equation: $y = \frac { 6 ( x - 6 ) } { x + 5 }$
Inequality: $y \leq 0$

A) $- 5 \leq x \leq 6$
B) $- 5 < x > 6$
C) $- 5 < x \leq 6$
D) $- 5 < x \leq 6$
E) $- 5 < x < 6$

Question 26

Find the domain of x in the expression.
$\sqrt { 9 - 4 x ^ { 2 } }$

A) $\left[ \frac { 3 } { 2 } , \frac { 3 } { 2 } \right]$
B) $\left[ - \frac { 3 } { 2 } , - \frac { 3 } { 2 } \right]$
C) $\left[ - \frac { 3 } { 2 } , \frac { 3 } { 2 } \right]$ .
D) $\left[ - \frac { 2 } { 3 } , \frac { 2 } { 3 } \right]$
E) $\left[ - \frac { 3 } { 2 } , - \frac { 3 } { 2 } \right]$ .

Question 27

Use a graphing utility to graph the equation.Use the graph to approximate the values of x that satisfy each inequality.
Equation: $y = \frac { 5 x ^ { 2 } } { x ^ { 2 } + 25 }$
Inequality: $y \leq 2$

A) $- \infty < x \leq \frac { 5 \sqrt { 3 } } { 3 }$
B) $- \infty < x < \infty$
C) $- \frac { 5 \sqrt { 3 } } { 3 } \leq x \leq \frac { 5 \sqrt { 3 } } { 3 }$
D) $- \infty < x \leq \frac { \sqrt { 3 } } { 3 }$
E) $- \infty < x \leq 5 \sqrt { 3 }$

Question 28

Find the domain of x in the expression.
$\sqrt { 25 - x ^ { 2 } }$

A) $( - 25,25 )$
B) $[ - 25,25 ]$
C) $( - 5,5 )$
D) $[ - 5,25 )$
E) $[ - 5,5 ]$

Question 29

Use a graphing utility to graph the equation.Use the graph to approximate the values of x that satisfy each inequality.
Equation: $y = x ^ { 3 } - x ^ { 2 } - 16 x + 16$
Inequality: $y \leq 0$

A) $\begin{array} { l } \infty < x \leq 4 \\1 \leq x \leq 4\end{array}$
B) $\begin{array} { l } \infty < x \leq - 4 \\1 \leq x \leq 4\end{array}$
C) $\begin{array} { l } - \infty < x \leq - 4 \\- 1 \leq x \leq - 4\end{array}$
D) $\begin{array} { l } - \infty < x \leq - 4 \\1 \leq x \leq 4\end{array}$
E) $- \infty < x \leq 4$

Question 30

Find the domain of x in the expression.
$\sqrt { \frac { x } { x ^ { 2 } - 2 x - 24 } }$

A) $( - 4,0 ] \cap ( 6 , \infty )$
B) $( - 6,0 ] \cup ( 4 , \infty )$
C) $( - 4,0 ] \cup ( 6 , \infty )$
D) $( - 4,0 ] \cup ( - 6 , \infty )$
E) $( - 6,0 ] \cap ( - 4 , \infty )$

Question 31

Find the domain of x in the expression.
$\sqrt { x ^ { 2 } - 4 }$

A) $( - \infty , 2 ] \cap [ 2 , \infty )$
B) $( - \infty , - 2 ] \cup [ 2 , \infty )$
C) $( - \infty , - 2 ] \cap [ 2 , \infty )$
D) $( - \infty , 2 ] \cup [ 2 , \infty )$
E) $( - \infty , - 2 ) \cup [ 2 , \infty )$

Question 32

Solve the inequality and graph the solution on the real number line.
$\frac { 1 } { x } \geq \frac { 1 } { x + 2 }$

A) $( - \infty , - 2 ) \cap ( 0 , \infty )$
B) $( - \infty , - 2 ) \cup ( 0 , \infty )$
C) $( - \infty , 2 ) \cap ( 0 , \infty )$
D) $( \infty , 2 ) \cup ( 0 , \infty )$
E) $( - \infty , 2 ) \cup ( 0 , \infty )$

Question 33

Use a graphing utility to graph the equation.Use the graph to approximate the values of x that satisfy each inequality.
Equation: $y = \frac { 6 x } { x - 5 }$
Inequality: $y \geq 8$

A) $5 < x \leq - \frac { 10 } { 1 }$
B) $5 < x \leq \frac { 10 } { 1 }$
C) $5 < x$
D) $5 < x \leq \frac { 10 } { 1 }$
E) $6 < x \leq \frac { 10 } { 1 }$

Question 34

Find the domain of x in the expression.
$\sqrt { \frac { x } { x ^ { 2 } - 36 } }$

A) $( - 36,0 ] \cup ( 36 , \infty )$
B) $( - 36,0 ] \cap ( 36 , \infty )$
C) $( - 36,0 ] \cap ( 6 , \infty )$
D) $( - 6,0 ] \cup ( 6 , \infty )$
E) $( - 36,0 ] \cap ( - 6 , \infty )$

Question 35

Solve the inequality and graph the solution on the real number line.
$\frac { x ^ { 2 } + 4 x } { x ^ { 2 } - 25 } \leq 0$

A) $( - 5 , - 4 ] \cup [ 0,5 )$
B) $( - 5,4 ] \cup [ 0 , - 5 )$
C) $( - 5,4 ] \cup [ 0,5 )$
D) $( 5 , - 4 ] \cup [ 0,5 )$
E) $( 5,4 ] \cup [ 0,5 )$

Question 36

Solve the inequality and graph the solution on the real number line. $\frac { 3 x - 5 } { x - 5 } \geq 0$

A)( $- \infty , \frac { 5 } { 3 }$ ] $\text { U } ( 5 , \infty )$
B)( $- \infty , \frac { 5 } { 3 }$ ] $\cup ( - 5 , \infty )$
C)( $- \infty , - \frac { 5 } { 3 }$ ] $\text { U } ( 5 , \infty )$
D)( $- \infty , - \frac { 5 } { 3 }$ ] $\cup ( - 5 , \infty )$
E)( $- \infty , \frac { 5 } { 3 }$ ] $\cap ( 5 , \infty )$

Question 37

Solve the inequality and graph the solution on the real number line.
$\frac { x + 9 } { x + 1 } - 2 < 0$

A) $( - \infty , - 1 ) \cup ( 7 , \infty )$
B) $( - \infty , - 1 ) \cap ( - 7 , \infty )$
C) $( - \infty , 1 ) \cap ( 7 , \infty )$
D) $( - \infty , - 1 ) \cup ( - 7 , \infty )$
E) $( - \infty , - 1 ) \cap ( 7 , \infty )$

Question 38

Solve the inequality and graph the solution on the real number line.
$\frac { 2 } { x + 4 } > \frac { 1 } { x - 2 }$

A) $( - 4,2 ) \cup ( 8 , \infty )$
B) $( - 4,2 ) \cap ( 8 , \infty )$
C) $( - 4 , - 2 ) \cup ( 8 , \infty )$
D) $( - 4,2 ) \cap ( - 8 , \infty )$
E) $( 4,2 ) \cup ( 8 , \infty )$

Question 39

Use a graphing utility to graph the equation.Use the graph to approximate the values of x that satisfy the inequality.
Equation: $y = \frac { 1 } { 6 } x ^ { 2 } - 6 x + 1$
Inequality: $y \leq 0$

A) $x \leq - 1 - \sqrt { \frac { 4 } { 27 } } , 1 - \sqrt { \frac { 4 } { 27 } } \leq x \leq 1 + \sqrt { \frac { 4 } { 27 } }$
B) $1 - \sqrt { \frac { 4 } { 27 } } \leq \mathrm { x } \leq 1 + \sqrt { \frac { 4 } { 27 } }$
C) $x \leq 1 - \sqrt { \frac { 4 } { 27 } } , 1 + \sqrt { \frac { 4 } { 27 } } \leq x$
D) $x \leq - 1 - \sqrt { \frac { 4 } { 27 } } , - 1 + \sqrt { \frac { 4 } { 27 } } \leq x$
E) $- 1 - \sqrt { \frac { 4 } { 27 } } \leq x \leq - 1 + \sqrt { \frac { 4 } { 27 } }$

Question 40

Solve the inequality and write the solution set in interval notation.
$x ^ { 8 } ( x - 2 ) \leq 0$

A) $( - \infty , 2 ]$
B) $( - \infty , - 2 ) ]$
C) $( - \infty , 2 ]$ .
D) $( - 2,2 ]$
E) $( - \infty , 2 )$

Question 41

Solve the inequality $36 x - x ^ { 3 } < 0$ and write the solution set in interval notation.

A) $( - \infty , - 6 ) \cup ( 0,6 )$
B) $( - 6,6 )$
C) $( - \infty , 6 )$
D) $( - 6,0 ) \cup ( 6 , \infty )$
E) $( - \infty , \infty )$

Question 42

Find the interval(s) for b such that the equation has at least one real solution and write a conjecture about the interval(s) based on the values of the coefficients
$4 x ^ { 2 } + b x + 7 = 0$ .

A) $( - \infty , - 2 \sqrt { 28 } ] \cap [ 2 \sqrt { 28 } , \infty )$ If $a > 0$ and $c < 0$ , $b \geq - 2 \sqrt { a c }$ or $b \geq 2 \sqrt { a c }$
B) $( - \infty , - 2 \sqrt { 28 } ] \cup [ - 2 \sqrt { 28 } , \infty )$ If $a < 0$ and $c > 0$ , $b \leq - 2 \sqrt { a c }$ or $b \leq 2 \sqrt { a c }$
C) $( - \infty , - 2 \sqrt { 28 } ] \cup [ 2 \sqrt { 28 } , \infty )$ If $a > 0$ and $c > 0$ , $b \leq - 2 \sqrt { a c }$ or $b \geq 2 \sqrt { a c }$
D) $( - \infty , 2 \sqrt { 28 } ] \cup [ 2 \sqrt { 28 } , \infty )$ If $a > 0$ and $c > 0$ , $b \leq 2 \sqrt { a c }$ or $b \geq 2 \sqrt { a c }$
E) $( - \infty , - 2 \sqrt { 28 } ] \cap [ 2 \sqrt { 28 } , \infty )$ If $a < 0$ and $c < 0$ , $b \leq 2 \sqrt { a c }$ or $b \leq 2 \sqrt { a c }$

Question 43

Find the domain of x in the expression $\sqrt [ 4 ] { x ^ { 3 } - 3 x }$ .

A) $( - \infty , - \sqrt { 3 } ] , [ \sqrt { 3 } , \infty )$
B) $( - \infty , \sqrt { 3 } ] , [ \sqrt { 3 } , \infty )$
C) $[ - \sqrt { 3 } , 0 ] , [ \sqrt { 3 } , \infty )$
D) $[ - \sqrt { 3 } , \sqrt { 3 } ]$
E) $( - \infty , - \sqrt { 3 } ) , ( 0 , \sqrt { 3 } )$

Question 44

Determine the equations of the vertical and horizontal asymptotes of the graph of the function $f ( x ) = \frac { x } { x - 4 }$ .

A)horizontal: y = 0 ; vertical: x = 4
B)horizontal: y = -4 ; vertical: x = 0
C)horizontal: x = 0; vertical: y = 4
D)horizontal: x = 4 ; vertical: y = -1
E)horizontal: y = 1 ; vertical: x = 4

Question 45

A rectangular playing field with a perimeter of 98 meters is to have an area of at least 444 square meters.Within what bounds must the length of the rectangle lie?

A) $444 m \leq L \leq 13 m$
B) $37 m \leq L \leq 98 m$
C) $12 m \leq L \leq 37 m$
D) $39 m \leq L \leq 14 m$
E) $444 m < L < 13 m$

Question 46

Find the domain of the function $f ( x ) = \frac { 9 } { x - 8 }$ .

A)Domain: all real numbers x except x = 8
B)Domain: all real numbers x except x = 9
C)Domain: all real numbers x except x = -9
D)Domain: all real numbers x
E)Domain: all real numbers x except x = -8

Question 47

Determine the intervals on which the following polynomial is entirely negative and those on which it is entirely positive. $- x ^ { 2 } - 2 x + 35$

A)entirely negative: $( - \infty , 6 )$ ; entirely positive: $( 6 , \infty )$
B)entirely negative: $( - \infty , - 7 ) , ( 5,6 )$ ; entirely positive: $( - 7,6 )$
C)entirely negative: $( - \infty , - 7 ) , ( 5 , \infty )$ ; entirely positive: $( - 7,5 )$
D)entirely negative: $( - 7,6 )$ ; entirely positive: $( 0 , \infty )$
E)entirely negative: $( - \infty , 0 )$ ; entirely positive: $( 0 , \infty )$

Question 48

Find the domain of x in the following expression. $\sqrt [ 3 ] { x ^ { 4 } - 625 }$

A) $[ - 5,5 ]$
B) $( - \infty , 5 ) \cup ( 5 , \infty )$
C) $[ 5 , \infty )$
D) $( 5 , \infty )$
E)all real numbers

Question 49

the solution set of the inequality $\frac { 7 } { 2 } x ^ { 2 } + 7 x + 14 \geq 0$ is the entire set of real numbers.

Question 50

Find the domain of the function $f ( x ) = \frac { 6 x ^ { 2 } } { x ^ { 2 } - 25 }$ .

A)Domain: all real numbers x except x = 5
B)Domain: all real numbers x except x = ±25
C)Domain: all real numbers x except x = ±6
D)Domain: all real numbers x except x = -5
E)Domain: all real numbers x except x = ±5

Question 51

Use the position equation $s = - 16 t ^ { 2 } + v _ { 0 } t + s _ { 0 }$ , where $S$ represents the height of an object (in feet), $v_0$ represents the initial velocity of the object (in feet per second), $s_0$ represents the initial height of the object (in feet), and t represents the time (in seconds). A projectile is fired straight upward from ground level $\left( s _ { 0 } = 0 \right)$ with an initial velocity of 176 feet per second.At what instant will it be back at ground level?

A) $t = 11$ Sec
B) $t = 16$ Sec
C) $t = 13$ Sec
D) $t = 12$ Sec
E) $t = 10$ Sec

Question 52

The graph of the function $f ( x ) = \frac { 3 } { x - 2 }$ is shown below.Determine the vertical and horizontal asymptotes of its graph.

A)horizontal: y = 0; vertical: x = 2
B)horizontal: y = 0; vertical: x = -2
C)horizontal: y = -2; vertical: x = 0
D)horizontal: y = 2; vertical: x = 0
E)horizontal: y = -2; vertical: x = 2

Question 53

Find the interval(s) for b such that the following equation has at least one real solution
$x ^ { 2 } + b x + 6 = 0$ .

A) $( - \infty , - \sqrt { 24 } ] \cup [ \sqrt { 24 } , \infty )$
B) $( - \infty , - \sqrt { 24 } ] \cap [ \sqrt { 24 } , \infty )$
C) $( - \infty , \sqrt { 24 } ] \cup ( \sqrt { 24 } , \infty )$
D) $( - \infty , - \sqrt { 24 } ) \cup [ - \sqrt { 24 } , \infty )$
E) $( - \infty , \sqrt { 24 } ] \cap [ \sqrt { 24 } , \infty )$

Question 54

A rectangular parking lot with a perimeter of 442 feet is to have an area of at least 8050 square feet.Within what bounds must the length of the rectangle lie?

A) $8050 \mathrm { ft } \leq L \leq 442 \mathrm { ft }$
B) $177 \mathrm { ft } \leq L \leq 48 \mathrm { ft }$
C) $49 \mathrm { ft } \leq L \leq 178 \mathrm { ft }$
D) $8050 \mathrm { ft } \leq L \leq 47 \mathrm { ft }$
E) $46 \mathrm { ft } \leq L \leq 175 \mathrm { ft }$

Question 55

Solve: $x ^ { 2 } - 2 x - 15 < 0$

A) $( - \infty , - 2 )$
B) $( - 3 , \infty )$
C) $( - 3,5 )$
D) $( - \infty , 5 )$
E) $( 5 , \infty )$

Question 56

Determine the equations of the vertical and horizontal asymptotes of the graph of the function $f ( x ) = \frac { 1 } { x - 5 }$ .

A)horizontal: y = 1; vertical: x = 5
B)horizontal: x = 0; vertical: y = 5
C)horizontal: y = -5; vertical: x = 0
D)horizontal: x = 5; vertical: y = -1
E)horizontal: y = 0; vertical: x = 5

Question 57

Use the position equation $s = - 16 t ^ { 2 } + v _ { 0 } t + s _ { 0 }$ , where s represents the height of an object (in feet), $v _ { 0 }$ represents the initial velocity of the object (in feet per second), $s_0$ represents the initial height of the object (in feet), and t represents the time (in seconds). A projectile is fired straight upward from ground level $\left( s _ { 0 } = 0 \right)$ with an initial velocity of 160 feet per second.At what instant will it be back at ground level?

A) $t = 8$ Sec
B) $t = 10$ Sec
C) $t = 12$ Sec
D) $t = 11$ Sec
E) $t = 9$ Sec

Question 58

Find the domain of x in the expression $\sqrt { 16 - x ^ { 2 } }$ .

A) $( - \infty , - 4 ] \cup [ 4 , \infty )$
B) $( - \infty , 4 ]$
C) $[ - 4,4 ]$
D) $[ - 4 , \infty )$
E) $( - \infty , \infty )$

Question 59

Find the interval(s) for b such that the following equation has at least one real solution and write a conjecture about the interval(s) based on the values of the coefficients
$4 x ^ { 2 } + b x + 13 = 0$ .

A) $( - \infty , - 2 \sqrt { 52 } ] \cup [ 2 \sqrt { 52 } , \infty )$ If $a > 0$ and $c > 0$ , $b \leq - 2 \sqrt { a c }$ or $b \geq 2 \sqrt { a c }$
B) $( - \infty , - 2 \sqrt { 52 } ] \cup [ - 2 \sqrt { 52 } , \infty )$ If $a > 0$ and $c < 0$ , $b \leq - 2 \sqrt { a c }$ or $b \geq 2 \sqrt { a c }$
C) $( - \infty , 2 \sqrt { 52 } ] \cup [ 2 \sqrt { 52 } , \infty )$ If $a > 0$ and $c > 0$ , $- b \leq - 2 \sqrt { a c }$ or $b \leq 2 \sqrt { a c }$
D) $( - \infty , 2 \sqrt { 52 } ] \cap [ 2 \sqrt { 52 } , \infty )$ If $a < 0$ and $c > 0$ , $b \leq - 2 \sqrt { a c }$ or $b \geq 2 \sqrt { a c }$
E) $( - \infty , - 2 \sqrt { 52 } ] \cap [ 2 \sqrt { 52 } , \infty )$ If $a < 0$ and $c < 0$ , $b \leq 2 \sqrt { a c }$ or $b \geq 2 \sqrt { a c }$

Question 60

When two resistors of resistances $R _ { 1 }$ and $R _ { 2 }$ are connected in parallel (see figure), the total resistance $R$ satisfies the equation $$\frac { 1 } { R } = \frac { 1 } { R _ { 1 } } + \frac { 1 } { R _ { 2 } }$$ . Find $R _ { 1 }$ for a parallel circuit in which $R _ { 2 } = 7$ ohms and R must be at least 1 ohm.

A) $R _ { 1 } \leq 7 \text { ohms }$
B) $R _ { 1 } < 7 \text { ohms }$
C) $R _ { 1 } \geq$ $\frac { 7 } { 6 }$ $\text { ohms }$
D) $R _ { 1 } > 7 \mathrm { ohms }$
E) $R _ { 1 } =$ $\frac { 7 } { 6 }$ $\text { ohms }$

Question 61

The graph of the function
$$f ( x ) = \frac { 3 x } { x ^ { 2 } - 4 }$$ is shown below.Determine the domain.

A)Domain: all real numbers except x = -2 and x = 2
B)Domain: all real numbers except x = 2
C)Domain: all real numbers except x = 0
D)Domain: all real numbers except x = 1
E)Domain: all real numbers except x = 4

Question 62

Find the zeros (if any) of the rational function.
$f ( x ) = 1 - \frac { 8 } { x - 8 }$

A) 8
B)-1
C) -16
D)1
E) 16

Question 63

Determine the domain of the function $f ( x ) = \frac { 5 } { ( x - 2 ) ^ { 4 } }$ .

A)Domain: all real numbers except x = -5 and -2
B)Domain: all real numbers
C)Domain: all real numbers except x = -5 and 2
D)Domain: all real numbers except x = 2
E)Domain: all real numbers except x = 5 and 2

Question 64

Find the domain of the function and identify any vertical and horizontal asymptotes.
$f ( x ) = \frac { 25 } { x ^ { 2 } }$

A)Domain: all real numbers x except x = 0Vertical asymptote: x = 0Horizontal asymptote: y = 0
B) Domain: all real numbers x except x = 5Vertical asymptote: x = 0Horizontal asymptote: y = 0
C) Domain: all real numbers x except x = 25Vertical asymptote: x = 0Horizontal asymptote: y = 0
D) Domain: all real numbers xVertical asymptote: x = 0Horizontal asymptote: y = 0
E) Domain: all real numbers x except x = ±5Vertical asymptote: y = 0Horizontal asymptote: x = 0

Question 65

Determine the equations of the vertical and horizontal asymptotes of the graph of the function $f ( x ) = \frac { 5 x ^ { 2 } } { x ^ { 2 } - 4 }$ .

A)horizontal: y = -2; vertical: x = 5
B)horizontal: x = 2 and x = -2; vertical: y = -5
C)horizontal: y = 5; vertical: x = 2 and x = -2
D)horizontal: x = -5; vertical: y = 2 and y = -2
E)horizontal: y = 5; vertical: x = 2

Question 66

Find the domain of the function and identify any vertical and horizontal asymptotes.
$f ( x ) = \frac { 9 } { ( x - 3 ) ^ { 3 } }$

A)Domain: all real numbers xVertical asymptote: x = 0Horizontal asymptote: y = 0
B)Domain: all real numbers x except x = 9Vertical asymptote: x = 0Horizontal asymptote: y = 0
C)Domain: all real numbers x except x = 3Vertical asymptote: x = 0Horizontal asymptote: y = 9
D)Domain: all real numbers xVertical asymptote: x = 0Horizontal asymptote: y = 9
E)Domain: all real numbers x except x = 3Vertical asymptote: x = 3Horizontal asymptote: y = 0

Question 67

Find the domain of the function and identify any vertical and horizontal asymptotes. $f ( x ) = \frac { 5 x ^ { 2 } + 8 } { x ^ { 2 } + x + 9 }$

A)Domain: all real numbers x
Vertical asymptote: No vertical asymptoteHorizontal asymptote: y = 5
B)Domain: all real numbers except x = 0
Vertical asymptote: x = 0
Horizontal asymptote: y = -8
C)Domain: all real numbers x
Vertical asymptote: x = -5
Horizontal asymptote: y = 0
D)Domain: all real numbers except x = 5
Vertical asymptote: No vertical asymptote
Horizontal asymptote: No horizontal asymptote
E)Domain: all real numbers except x = 9
Vertical asymptote: x = 5
Horizontal asymptote: y = 8

Question 68

Find the domain of the function.
$g ( s ) = \frac { - 3 s } { s - 9 }$

A)s = 9
B)all real numbers s $\neq$ 9, s $\neq$ 0
C) s = 9, s = 0
D)all real numbers s $\neq$ 9
E) $\varnothing$

Question 69

Select the correct graph of the function $f ( x ) = \frac { 8 } { x - 2 }$ .

A)
B)
C)
D)
E)

Question 70

Find the zeros (if any) of the rational function.
$f ( x ) = 1 + \frac { 6 } { x ^ { 2 } - 7 }$

A)±7
B)±6
C)6
D)±1
E) 7

Question 71

Find the domain of the function and identify any vertical and horizontal asymptotes.
$f ( x ) = \frac { 2 x ^ { 2 } } { x + 3 }$

A)Domain: all real numbers x except x = 0Vertical asymptote: x = 0Horizontal asymptote: y = -2
B)Domain: all real numbers x except x = -3Vertical asymptote: x = -3Horizontal asymptote: No horizontal asymptote
C)Domain: all real numbers x except x = 3Vertical asymptote: x = 3Horizontal asymptote: No horizontal asymptote
D)Domain: all real numbers x except x = 3Vertical asymptote: x = 3Horizontal asymptote: y = 2
E)Domain: all real numbers xVertical asymptote: x = -3Horizontal asymptote: y = 0

Question 72

Find the domain of the function and identify any vertical and horizontal asymptotes.
$f ( x ) = \frac { x ^ { 3 } } { x ^ { 2 } - 49 }$

A)Domain: all real numbers x except x = 0Vertical asymptote: x = ±7Horizontal asymptote: No horizontal asymptote
B)Domain: all real numbers x except x = ±7Vertical asymptote: x = ±7Horizontal asymptote: No horizontal asymptote
C)Domain: all real numbers x except x = 7Vertical asymptote: x = 7Horizontal asymptote: y = 7
D)Domain: all real numbers xVertical asymptote: x = -7Horizontal asymptote: y = 0
E)Domain: all real numbers x except x = 0Vertical asymptote: x = 0Horizontal asymptote: y = -49

Question 73

Determine the zeros (if any) of the rational function $g ( x ) = 6 + \frac { 3 } { x ^ { 2 } + 6 }$ .

A)x = -6, x = 6
B) $x = - \sqrt { 6 } , x = \sqrt { 6 }$
C) $x = - \frac { 1 } { 2 } , x = \frac { 1 } { 2 }$
D)x = -3
E)no zeros

Question 74

Find the domain of the function and identify any vertical and horizontal asymptotes.
$f ( x ) = \frac { 7 + x } { 7 - x }$

A)Domain: all real numbers x except x = 7Vertical asymptote: x = 7Horizontal asymptote: y = -1
B)Domain: all real numbers xVertical asymptote: x = -7Horizontal asymptote: y = 0
C)Domain: all real numbers x except x = 0Vertical asymptote: x = 0Horizontal asymptote: y = -1
D)Domain: all real numbers x except x = 7Vertical asymptote: x = 0Horizontal asymptote: y = -7
E)Domain: all real numbers x except x = -7Vertical asymptote: x = 0Horizontal asymptote: y = 7

Question 75

Find the zeros (if any) of the rational function.
$g ( x ) = \frac { x ^ { 2 } - 25 } { x + 5 }$

A)-25
B)±5
C)-5
D)25
E)5

Question 76

Select the correct graph of the function $f ( x ) = \frac { 6 } { x + 4 }$ .

A)
B)
C)
D)
E)

Question 77

Determine the zeros (if any) of the rational function $f ( x ) = \frac { x ^ { 2 } - 4 } { x - 4 }$ .

A)x = -4, x = 4
B)no zeros
C)x = -3
D) $x = - \frac { 2 } { 3 } , x = \frac { 2 } { 3 }$
E)x = -2, x = 2

Question 78

Select the correct graph of the function $f ( x ) = \frac { x - 4 } { x - 7 }$ .

A)
B)
C)
D)
E)

Question 79

Find the zeros (if any) of the rational function.
$f ( x ) = 2 + \frac { 12 } { x ^ { 2 } + 2 }$

A)-2
B)2
C)8
D)-8
E)None

Question 80

Select the graph of the rational function $f ( x ) = - \frac { x + 6 } { x + 7 }$ .

A)
B)
C)
D)
E)