Question 1

Graph the function with a graphing utility.
-$y = \frac { x + 1 } { x ^ { 2 } + x - 30 }$

Accepted Answer

The answer of Graph the function with a graphing utility.
-\(y...

Question 2

Provide an appropriate response.
-If the ordered pair $( 6,2 )$ belongs to function $g$, then $gـــــــ ( \quad ) =ـــــــ$

Accepted Answer

In the context of functions, an ordered pair $(x, y)$ is typically written with the input or independent variable $x$ first, followed by the output or dependent variable $y$. Therefore, if the ordered pair $(6, 2)$ belongs to function $g$, it means that when the input is $6$, the output is $2$, which is correctly represented as $g(6) = 2$.

Question 3

Graph the function with a graphing utility.
-$y=x^{3}-1$

Accepted Answer

The answer of Graph the function with a graphing utility.
-$y=x^{3}-1$

...

Question 4

Graph the function with a graphing utility.
-$y = \frac { - 4 } { x - 6 }$

Accepted Answer

The answer of Graph the function with a graphing utility.
-\(y...

Question 5

Graph the function with a graphing utility.
-$y=x^{2}+2 x-7$

Accepted Answer

The answer of Graph the function with a graphing utility.
-\(y=x^{2}+2...

Question 6

Provide an appropriate response.
-Consider the linear function f(x) $f ( x ) = 5 x + 20$ 20. What is the domain and range of this function? Now, suppose the
function represents the relationship between studying time and grades on an exam. The variable x represents
the number of hours spent studying and f(x) represents the grade on the exam. Does this change the domain
and range? If so, what is the new domain and range and why is it different?

Accepted Answer

The answer of Provide an appropriate response.
-Consider the linear function...

Question 7

Provide an appropriate response.
-Give a definition of Range.

Accepted Answer

The answer of Provide an appropriate response.
-Give a definition of...

Question 8

Crafty Bill's Cool Car Sales opened as a used car sales lot in 2006. The graph shows the number of cars sold f as a function of time t. Find and interpret f(2010).

Accepted Answer

The answer of Crafty Bill's Cool Car Sales opened as...

Question 9

Graph the function with a graphing utility.
-$$y = - x ^ { 2 } + 2 x - 5$$

Accepted Answer

The answer of Graph the function with a graphing utility.
-\[y...

Question 10

Provide an appropriate response.
-Suppose the population of deer fluctuates over time. The population increases in the summer and decreases in
the winter. It also varies over many years as well. If you looked at the graph of population versus time, would
this relation be a function? Why or why not?

Accepted Answer

The answer of Provide an appropriate response.
-Suppose the population of...

Question 11

The function $\mathrm { E } ( \mathrm { x } ) = 0.0036 \mathrm { x } ^ { 3 } + 0.0055 \mathrm { x } ^ { 2 } + 0.19 \mathrm { x } + 1.76$ gives the approximate total earnings of a company, in millions of dollars, where $x = 0$ corresponds to $2006 , x = 1$ corresponds to 2007 , and so on. This model is valid for the years from 2006 to 2010 . Determine the earnings for 2007. Round to two decimal places if necessary.

Accepted Answer

The earnings for 2007 correspond to $x = 1$. Substituting this value into the given function, we get:$\mathrm { E } ( 1 ) = 0.0036 ( 1 ) ^ { 3 } + 0.0055 ( 1 ) ^ { 2 } + 0.19 ( 1 ) + 1.76$$\mathrm { E } ( 1 ) = 0.0036 + 0.0055 + 0.19 + 1.76$$\mathrm { E } ( 1 ) = 1.9591$Rounding to two decimal places, the earnings for 2007 are $1.96 million.

Question 12

Graph the function with a graphing utility.
-$y = x ^ { 4 } + 2 x ^ { 2 } - 2$

Accepted Answer

The answer of Graph the function with a graphing utility.
-\(y...

Question 13

Employees of a publishing company received an increase in salary of 7% plus a bonus of $700. Let S(x) = 1.07x + 700 represent the new salary in terms of the previous salary x. Find and interpret S(13,000).

Accepted Answer

To find the new salary, substitute $13,000 into the given formula: S(13,000) = 1.07(13,000) + 700 = $14,610. This means an employee's new salary, after a 7% increase and a $700 bonus on a $13,000 salary, is $14,610.

Question 14

Graph the function with a graphing utility.
-$y=x^{2}+3$

Accepted Answer

The answer of Graph the function with a graphing utility.
-$y=x^{2}+3$

...

Question 15

The bar graph below gives the number of births in a certain state for the months October to April, where $t = 1$ corresponds to October and $t = 7$ corresponds to April. If the number of births in thousands in this state is the function $B ( t )$, where $t$ is in months, find $B ( 4 )$ and explain its meaning.

Accepted Answer

The answer of The bar graph below gives the number...

Question 16

Graph the function with a graphing utility.
-$y=x^{3}+x^{2}+2 x-1$

Accepted Answer

The answer of Graph the function with a graphing utility.
-\(y=x^{3}+x^{2}+2...

Question 17

Suppose a cost-benefit model is given by $C ( p ) = \frac { 5.8 p } { 100 - p }$ , where C is the cost in thousands of dollars for removing p percent of a given pollutant. Find C(90) to the nearest dollar and interpret it.

Accepted Answer

Plugging p = 90 into the given formula $C(90) = \frac{5.8 \times 90}{100 - 90} = \frac{522}{10} = 52.2$ thousand dollars, or $52,200, for removing 90% of the pollutant.

Question 18

Graph the function with a graphing utility.
-$y=5 x^{2}$

Accepted Answer

The answer of Graph the function with a graphing utility.
-\(y=5...

Question 19

Crafty Bill's Cool Car Sales opened as a used car sales lot in 2006. The graph shows the number of cars sold as a function of time. What is the approximate number of cars sold in 2008?

Accepted Answer

The answer of Crafty Bill's Cool Car Sales opened as...

Question 20

Provide an appropriate response.
-Describe the graph of the function $\mathrm { f } ( \mathrm { x } ) = \mathrm { x } + 3$ if the domain is $\{ 3,4,5,6 \}$.

Accepted Answer

The function $f(x) = x + 3$ adds 3 to each x-value in the domain $\{3,4,5,6\}$, resulting in the points $(3,6)$, $(4,7)$, $(5,8)$, and $(6,9)$.

Quiz 1: Functions, Graphs, and Models; Linear Functions

Graph the function with a graphing utility. - $y = \frac { x + 1 } { x ^ { 2 } + x - 30 }$ $Graph the function with a graphing utility. - y = \frac { x + 1 } { x ^ { 2 } + x - 30 } A) B) C) D)$

Provide an appropriate response. -If the ordered pair $( 6,2 )$ belongs to function $g$ , then $gـــــــ ( \quad ) =ـــــــ$

Graph the function with a graphing utility. - $y=x^{3}-1$ $Graph the function with a graphing utility. - y=x^{3}-1 A) B) C) D)$

Graph the function with a graphing utility. - $y = \frac { - 4 } { x - 6 }$ $Graph the function with a graphing utility. - y = \frac { - 4 } { x - 6 } A) B) C) D)$

Graph the function with a graphing utility. - $y=x^{2}+2 x-7$ $Graph the function with a graphing utility. - y=x^{2}+2 x-7 A) B) C) D)$

Provide an appropriate response. -Give a definition of Range.

Crafty Bill's Cool Car Sales opened as a used car sales lot in 2006. The graph shows the number of cars sold f as a function of time t. Find and interpret f(2010) .

Graph the function with a graphing utility. - $y = - x ^ { 2 } + 2 x - 5$ $Graph the function with a graphing utility. - y = - x ^ { 2 } + 2 x - 5 A) B) C) D)$

Provide an appropriate response. -Suppose the population of deer fluctuates over time. The population increases in the summer and decreases in the winter. It also varies over many years as well. If you looked at the graph of population versus time, would this relation be a function? Why or why not?

Graph the function with a graphing utility. - $y = x ^ { 4 } + 2 x ^ { 2 } - 2$ $Graph the function with a graphing utility. - y = x ^ { 4 } + 2 x ^ { 2 } - 2 A) B) C) D)$

Employees of a publishing company received an increase in salary of 7% plus a bonus of $700. Let S(x) = 1.07x + 700 represent the new salary in terms of the previous salary x. Find and interpret S(13,000) .

Graph the function with a graphing utility. - $y=x^{2}+3$ $Graph the function with a graphing utility. - y=x^{2}+3 A) B) C) D)$

Graph the function with a graphing utility. - $y=x^{3}+x^{2}+2 x-1$ $Graph the function with a graphing utility. - y=x^{3}+x^{2}+2 x-1 A) B) C) D)$

Suppose a cost-benefit model is given by $C ( p ) = \frac { 5.8 p } { 100 - p }$ , where C is the cost in thousands of dollars for removing p percent of a given pollutant. Find C(90) to the nearest dollar and interpret it.

Graph the function with a graphing utility. - $y=5 x^{2}$ $Graph the function with a graphing utility. - y=5 x^{2} A) B) C) D)$

Crafty Bill's Cool Car Sales opened as a used car sales lot in 2006. The graph shows the number of cars sold as a function of time. What is the approximate number of cars sold in 2008?

Provide an appropriate response. -Describe the graph of the function $\mathrm { f } ( \mathrm { x } ) = \mathrm { x } + 3$ if the domain is $\{ 3,4,5,6 \}$ .

Quiz 1: Functions, Graphs, and Models; Linear Functions

Graph the function with a graphing utility. - y=x+1x2+x−30y = \frac { x + 1 } { x ^ { 2 } + x - 30 }y=x2+x−30x+1​

Provide an appropriate response. -If the ordered pair (6,2) ( 6,2 ) (6,2) belongs to function ggg , then gـــــــ() =ـــــــgـــــــ ( \quad ) =ـــــــgـــــــ() =ـــــــ

Graph the function with a graphing utility. - y=x3−1y=x^{3}-1y=x3−1

Graph the function with a graphing utility. - y=−4x−6y = \frac { - 4 } { x - 6 }y=x−6−4​

Graph the function with a graphing utility. - y=x2+2x−7y=x^{2}+2 x-7y=x2+2x−7

Provide an appropriate response. -Give a definition of Range.

Crafty Bill's Cool Car Sales opened as a used car sales lot in 2006. The graph shows the number of cars sold f as a function of time t. Find and interpret f(2010) .

Graph the function with a graphing utility. - y=−x2+2x−5y = - x ^ { 2 } + 2 x - 5y=−x2+2x−5

Provide an appropriate response. -Suppose the population of deer fluctuates over time. The population increases in the summer and decreases in the winter. It also varies over many years as well. If you looked at the graph of population versus time, would this relation be a function? Why or why not?

Graph the function with a graphing utility. - y=x4+2x2−2y = x ^ { 4 } + 2 x ^ { 2 } - 2y=x4+2x2−2

Employees of a publishing company received an increase in salary of 7% plus a bonus of $700. Let S(x) = 1.07x + 700 represent the new salary in terms of the previous salary x. Find and interpret S(13,000) .

Graph the function with a graphing utility. - y=x2+3y=x^{2}+3y=x2+3

Graph the function with a graphing utility. - y=x3+x2+2x−1y=x^{3}+x^{2}+2 x-1y=x3+x2+2x−1

Suppose a cost-benefit model is given by C(p) =5.8p100−pC ( p ) = \frac { 5.8 p } { 100 - p }C(p) =100−p5.8p​ , where C is the cost in thousands of dollars for removing p percent of a given pollutant. Find C(90) to the nearest dollar and interpret it.

Graph the function with a graphing utility. - y=5x2y=5 x^{2}y=5x2

Crafty Bill's Cool Car Sales opened as a used car sales lot in 2006. The graph shows the number of cars sold as a function of time. What is the approximate number of cars sold in 2008?

Provide an appropriate response. -Describe the graph of the function f(x) =x+3\mathrm { f } ( \mathrm { x } ) = \mathrm { x } + 3f(x) =x+3 if the domain is {3,4,5,6}\{ 3,4,5,6 \}{3,4,5,6} .

Graph the function with a graphing utility. - $y = \frac { x + 1 } { x ^ { 2 } + x - 30 }$ $Graph the function with a graphing utility. - y = \frac { x + 1 } { x ^ { 2 } + x - 30 } A) B) C) D)$

Provide an appropriate response. -If the ordered pair $( 6,2 )$ belongs to function $g$ , then $gـــــــ ( \quad ) =ـــــــ$

Graph the function with a graphing utility. - $y=x^{3}-1$ $Graph the function with a graphing utility. - y=x^{3}-1 A) B) C) D)$

Graph the function with a graphing utility. - $y = \frac { - 4 } { x - 6 }$ $Graph the function with a graphing utility. - y = \frac { - 4 } { x - 6 } A) B) C) D)$

Graph the function with a graphing utility. - $y=x^{2}+2 x-7$ $Graph the function with a graphing utility. - y=x^{2}+2 x-7 A) B) C) D)$

Graph the function with a graphing utility. - $y = - x ^ { 2 } + 2 x - 5$ $Graph the function with a graphing utility. - y = - x ^ { 2 } + 2 x - 5 A) B) C) D)$

Graph the function with a graphing utility. - $y = x ^ { 4 } + 2 x ^ { 2 } - 2$ $Graph the function with a graphing utility. - y = x ^ { 4 } + 2 x ^ { 2 } - 2 A) B) C) D)$

Graph the function with a graphing utility. - $y=x^{2}+3$ $Graph the function with a graphing utility. - y=x^{2}+3 A) B) C) D)$

Graph the function with a graphing utility. - $y=x^{3}+x^{2}+2 x-1$ $Graph the function with a graphing utility. - y=x^{3}+x^{2}+2 x-1 A) B) C) D)$

Suppose a cost-benefit model is given by $C ( p ) = \frac { 5.8 p } { 100 - p }$ , where C is the cost in thousands of dollars for removing p percent of a given pollutant. Find C(90) to the nearest dollar and interpret it.

Graph the function with a graphing utility. - $y=5 x^{2}$ $Graph the function with a graphing utility. - y=5 x^{2} A) B) C) D)$

Provide an appropriate response. -Describe the graph of the function $\mathrm { f } ( \mathrm { x } ) = \mathrm { x } + 3$ if the domain is $\{ 3,4,5,6 \}$ .