Deck 3: Linear, Quadratic, Polynomial, and Rational Functions

Question 1

Write the domain of the function r(x) as a union of intervals.

A)

B)

C)

D)

Answer 1

Question 2

Write the domain of the function r(x) as a union of intervals.

Answer 2

Question 3

Suppose
and . Write the expression (p + q)(x) as a ratio, with the numerator and denominator each written as a sum of terms of the form cx^m.

Answer 3

Question 4

Suppose
and . Write the expression (p + r)(x) as a ratio, with the numerator and denominator each written as a sum of terms of the form cx^m.

Question 5

Suppose
and . Write the expression (3p - 15r)(x) as a ratio, with the numerator and denominator each written as a sum of terms of the form cx^m.

Question 6

Suppose
and . Write the expression (pq)(x) as a ratio, with the numerator and denominator each written as a sum of terms of the form cx^m.

Question 7

Suppose . Write the expression (r(x))² as a ratio, with the numerator and denominator each written as a sum of terms of the form cx^m.

A)
B)
C)
D)

Question 8

Suppose
and . Write the expression (q(x))² p(x) as a ratio, with the numerator and denominator each written as a sum of terms of the form cx^m.

Question 9

Suppose
and . Write the expression as a ratio, with the numerator and denominator each written as a sum of terms of the form cx^m.

Question 10

Suppose
and . Write the expression as a ratio, with the numerator and denominator each written as a sum of terms of the form cx^m.

Question 11

Suppose
. Write the expression as a ratio, with the numerator and denominator each written as a sum of terms of the form cx^m.

Question 12

What is the domain of ?

A)
B)
C)
D)

Question 13

Find two distinct numbers x such that
, where
.

Question 14

What is the range of s, where s is defined by
?

Question 15

Write the expression
in the form , where q is the denominator of the given expression and G and R are polynomials with deg R < deg q.

Question 16

Write the expression
in the form , where q is the denominator of the given expression and G and R are polynomials with deg R < deg q.

Question 17

Write the expression
in the form , where q is the denominator of the given expression and G and R are polynomials with deg R < deg q.

Question 18

Find a constant c such that , where .

A) 4
B) 16
C) 0
D) -4

Question 19

Find the asymptotes of the graph of the function
.

A) y = 6
B) y = 0
C) x = 6
D) x = 0

Question 20

Find the asymptotes of the graph of the function

.

Question 21

Suppose p(x) = x² + 6x + 4, q(x) = 6x³ - 4x + 1. Write the expression (p + q)(x) as a sum of terms, each of which is a constant times a power of x.

A) 6x³ + x² + 2x + 5
B) 6x³ + x² + 2x - 5
C) 6x³ + x² - 2x + 5
D) 6x³ + x² - 2x - 5

Question 22

Suppose p(x) = x² + 9x + 7, r(x) = 18x³ + 9. Write the expression (9p - 7r)(x) as a sum of terms, each of which is a constant times a power of x.

Question 23

Suppose p(x) = x² + 3x + 1, r(x) = 6x³ + 3. Write the expression (p(x))²(r(x) - 3) as a sum of terms, each of which is a constant times a power of x.

Question 24

Suppose q(x) = 5x³ - 3x + 1, r(x) = 10x³ + 5. Write the expression
as a sum of terms, each of which is a constant times a power of x.

Question 25

Suppose p(x) = x² + 4x + 2, q(x) = 4x³ - 2x + 1, r(x) = 8x³ + 4. Write the expression as a sum of terms, each of which is a constant times a power of x.

Question 26

Suppose p(x) = x² + 8x + 6. Write the expression
As a sum of terms, each of which is a constant times a power of h.

A) 10 - h
B) 10 + h
C) -6 + h
D) -6 - h

Question 27

Find all real numbers x such that
x⁴ + 36x² - 2,592 = 0

Question 28

Find all real numbers x such that:

A) 4, 1
B) -4, 1
C) 4, -1
D) -4, -1

Question 29

Find all real numbers x such that:
x⁴ - 53x² + 196 = 0

Question 30

Suppose q(x) = $x^3 - 49x + b$ . The point (7, b) lies on the graph of q.

Question 31

is $x^8 - 1 = (x^4 + 1)(x^2 + 1)(x + 1)(x - 1)$ correct?

Question 32

Find a number b such that 6 is a zero of the polynomial p defined by p(x) = -36 + bx - 6x² + x³.

A) 36
B) -36
C) 6
D) -6

Question 33

Find a number b such that 1 is a zero of the polynomial p defined by p(x) = b - 9x + bx² + 9x³.

Question 34

Find a polynomial p of degree 3 such that -6, 6, and 7 are zeros of p and p(0) = 36. Write your answer in descending order by degree.

Question 35

Find a polynomial p of degree 3 such that -1,
, and 1 are zeros of p and p(0) = . Write your answer in descending order by degree.

Question 36

If p(x) = a²x² + 4x + 5 and q(x) = (1 - 2a)x² - 8x - 5, find a real number a such that (p + q)(x) has degree 1.

A) 4
B) -4
C) 0
D) 1

Question 37

Suppose d is a real number. Then $(d + 6)^4 = d^4 + 6^4$ if and only if d = 0

Question 38

The only possible integer zeros of $p(x) = 2x^5 - bx^3 + 4x - 2$ are 1 and 2.

Question 39

Find all choices of (b, c, d) such that 4 and 1 are the only zeros of the polynomial p(x) = x³ + bx² + cx + d.

Question 40

Find all choices of (b, c, d) such that 9 and -9 are the only zeros of the polynomial p(x) = x³ + bx² + cx + d.

Question 41

Factor x²⁴ - y¹² as nicely as possible.

Question 42

Evaluate the expression

.

Question 43

Write as a power of 3.

Question 44

Simplify the given expression by writing it as a power of a single variable.

Question 45

Simplify the given expression by writing it as a power of a single variable.

Question 46

Simplify the given expression by writing it as a power of a single variable.

Question 47

Write as a power of 2.

Question 48

Find integers m and n such that
.

Question 49

Simplify the given expression.

Question 50

Simplify the given expression.

Question 51

Simplify the given expression.

Question 52

Find a formula for if and
.

Question 53

Find a formula for if and
.

Question 54

Find the function which is graphed below

A)
B)
C)
D)

Question 55

Find the function which is graphed below.

A)
B)
C)
D)

Question 56

Find the function which is graphed below.

A)

B)

C) D)

Question 57

Find the function which is graphed below.

A)

B)

C)

D)

Question 58

Find the function which is graphed below.

A)

B)

C)

D)

Question 59

Evaluate the indicated quantity.25^3/2

A) 25
B) 5
C) 37.5
D) 125

Question 60

Evaluate the indicated quantity.(-512)^5/3

A) 32,768
B) -32,768
C) 512
D) Undefined

Question 61

Expand the indicated expression.

Question 62

Expand the indicated expression.

Question 63

Expand the indicated expression.

A)
B)
C)
D)

Question 64

Expand the indicated expression.

A)
B)
C)
D)

Question 65

Find a formula for the inverse function of the indicated function.

Question 66

Find a formula for the inverse function Of the indicated function.

A)

B)

C)

D)

Question 67

Find a formula for the inverse function of the indicated function.

A)
B)
C)
D)

Question 68

Find a formula for the inverse function
of the indicated function.

Question 69

Find a formula for (f g)(x) assuming that f and g are the indicated functions.
.

Question 70

Find a formula for (f g)(x) assuming that f and g are the indicated functions. and .

A)
B)
C)
D)

Question 71

Find all real numbers x such that satisfy the indicated equation.

Question 72

Find all real numbers x such that satisfy the indicated equation.

A)
And
B)

C)

D)

Question 73

Find all real numbers x such that satisfy the indicated equation.

Question 74

Suppose x is a number such that 2^x = 5. Evaluate 16^x.

A) 625
B) 20
C) 80
D) 40

Question 75

Evaluate the assuming that f and g are the functions defined by f(x) = 3^x and
.

Question 76

What is the domain of the function ? Write your answer using set builder notation.

Question 77

If x and y are irrational numbers, then xy is always an irrational number.

Question 78

If x and y are irrational numbers, then x + y may be a rational number.

Question 79

Find the vertex of the graph of the function

.

Question 80

Find the vertex of the graph of the function f(x) = (x - 11)² + 9.