Question 1

Use the slope-intercept form to write an equation of the line that passes through the given points. Use
function notation where y = f(x).
-$( 2 , - 3 )$ and $( - 7 , - 11 )$

Accepted Answer

A)  $f ( x ) = \frac { 9 } { 8 } x - \frac { 43 } { 9 }$ 
B)  $f ( x ) = \frac { 8 } { 9 } x - \frac { 43 } { 9 }$ 
C)  $f ( x ) = - \frac { 9 } { 8 } x - \frac { 1 } { 9 }$ 
D)  $f ( x ) = - \frac { 8 } { 9 } x - \frac { 1 } { 9 }$

Question 2

Find $\frac { f ( x + h ) - f ( x ) } { h }$ for the given function.
-$$f ( x ) = \frac { 1 } { x - 4 }$$

Accepted Answer

A)  $- \frac { 1 } { ( x - 4 ) ( x + h - 4 ) }$ 
B)  $\frac { 1 } { ( x - 4 ) ( x + h - 4 ) }$ 
C)  $- \frac { 1 } { 2 x + h - 8 }$ 
D)  $\frac { 1 } { 2 x + h - 8 }$

Question 3

Solve the problem.
-The population of a certain country since 1990 can be approximated by $f ( t ) = 0.008 t ^ { 2 } + 2.1 t + 175$ where $f ( t )$ is the population in millions and $t$ represents the number of years since 1990 . Find the average rate of change in the country's population between 1990 and 2010 . Round to 1 decimal place.

Accepted Answer

A)  $2.3$ million/yr 
B)  $2.0$ million/yr 
C)  $2.5$ million $/ \mathrm { yr }$ 
D)  $2.9 \mathrm { million } / \mathrm { yr }$

Question 4

Determine if the lines defined by the given equations are parallel, perpendicular, or neither.
-$$\begin{array} { l } 
- 4 y = 2 x + 5 \
- 4 x = 8 y + 3
\end{array}$$

Accepted Answer

A)  neither 
B)  parallel 
C)  perpendicular

Question 5

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-The distance from the center of a circle to any point on the circle is called the and is
often denoted by r.

Accepted Answer

The answer of Write the word or phrase that best...

Question 6

Sketch the graph using transformations of a parent function (without a table of values).
-$$h ( x ) = \sqrt [ 3 ] { x - 2 }$$

Accepted Answer

A) 
 
B) 
 
C) 
 
D)

Question 7

Solve the problem.
-A cell tower is a site where antennas, transmitters, and receivers are placed to create a cellular network. Suppose that a cell tower is located at a point A(-7, -6) on a map and its range is 2.5 mi. Write an equation that represents the boundary of the area that can receive a signal from the tower.
Assume that all distances are in miles.

Accepted Answer

A)  $( x + 7 ) ^ { 2 } + ( y + 6 ) ^ { 2 } = 6.25$ 
B)  $( x + 7 ) ^ { 2 } + ( y + 6 ) ^ { 2 } = 2.5$ 
C)  $| x + 7 | + | ( y + 6 ) | = 2.5$ 
D)  $| x - 7 | + | ( y - 6 ) | = 2.5$

Question 8

Determine which of the given points are solutions to the given equation.
-$$| x - 3 | - y = 2$$
I. $( 1,0 ) \quad$ II. $\left( \frac { 1 } { 4 } , \frac { 3 } { 4 } \right)$ III. $( - 5,10 )$

Accepted Answer

A)  II 
B)  III 
C)  $\mathrm { I }$ 
D)  I and II 
E)  I and III

Question 9

Evaluate the function for the indicated value, then simplify.
-$f ( x ) = x ^ { 2 } + 5 x$; find $f ( a + 1 )$, then simplify as much as possible.

Accepted Answer

A)  $a ^ { 2 } + 7 a + 6$ 
B)  $a ^ { 2 } + 7 a + 7$ 
C)  $a ^ { 2 } + 3 a + 2$ 
D)  $a ^ { 2 } + 3 a + 6$

Question 10

Determine the average rate of change of the function on the given interval.
-$$f ( x ) = 3 x ^ { 2 } + 3 \text { on } [ 3,5 ]$$

Accepted Answer

A)  $- 24$ 
B)  $\frac { 5 } { 2 }$ 
C)  24 
D)  $\frac { 3 } { 2 }$

Question 11

Choose the one alternative that best completes the statement or answers the question.
Graph the equation and identify the x- and y-intercepts.
-$$5 y + 1 = 21$$

Accepted Answer

A)  $x$-intercept: $( 4,0 ) ; y$-intercept: none
 
B)  $x$-intercept: none; $y$-intercept: $( 0 , - 4 )$
 
C)  $x$-intercept: $( - 4,0 ) ; y$-intercept: none
 
D)  $x$-intercept: none; $y$-intercept: $( 0,4 )$

Question 12

Estimate the x- and y-intercepts from the graph.
-

Accepted Answer

A)  $x$-intercepts: $( - 2,0 )$ and $( 2,0 )$; $y$-intercept: $( 0,4 )$ 
B)  $x$-intercept: $( 0,4 ) ; y$-intercepts: $( - 2,0 )$ and $( 2,0 )$ 
C)  $x$-intercept: $( 4,0 ) ; y$-intercepts: $( 0 , - 2 )$ and $( 0,2 )$ 
D)  $x$-intercepts: $( 0 , - 2 )$ and $( 0,2 ) ; y$-intercept: $( 4,0 )$

Question 13

Write an equation of the line satisfying the given conditions. Write the answer in slope-intercept form.
-The line passes through the point $( 15 , - 2 )$ and has a slope of $\frac { 2 } { 5 }$.

Accepted Answer

A)  $y = \frac { 2 } { 5 } x + 15$ 
B)  $y = \frac { 2 } { 5 } x + 22$ 
C)  $y = \frac { 2 } { 5 } x - 8$ 
D)  $y = - \frac { 2 } { 5 } x - 8$

Question 14

Use the given information about a circle to find its equation.
-Center $( - 5 , - 4 )$ and diameter 10

Accepted Answer

A)  $( x - 5 ) ^ { 2 } + ( y - 4 ) ^ { 2 } = 25$ 
B)  $( x + 5 ) ^ { 2 } + ( y + 4 ) ^ { 2 } = 100$ 
C)  $( x + 5 ) ^ { 2 } + ( y + 4 ) ^ { 2 } = 25$ 
D)  $( x - 5 ) ^ { 2 } + ( y - 4 ) ^ { 2 } = 100$

Question 15

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-A function defined by f (x) = mx + b is a function and its graph is a line in a
rectangular coordinate system.

Accepted Answer

The answer of Write the word or phrase that best...

Question 16

Find and simplify f (x + h).
-$$f ( x ) = x ^ { 3 } - 5 x + 8$$

Accepted Answer

A)  $x ^ { 3 } + 3 x ^ { 2 } h + 3 x h ^ { 2 } + h ^ { 3 } - 5 x - 5 h + 8$ 
B)  $x ^ { 3 } - 5 x + h + 8$ 
C)  $x ^ { 3 } + h ^ { 3 } - 5 x - 5 h + 8$ 
D)  $x ^ { 3 } - 5 x - 5 h + 8$

Question 17

A function g is given. Identify the parent function. Then use the steps for graphing multiple
transformations of functions to list, in order, the transformations applied to the parent function to obtain
the graph of g.
-$$g ( x ) = \frac { 1 } { 5 } ( x + 1.3 ) ^ { 2 } - 2.5$$

Accepted Answer

A)  Parent function: $f ( x ) = x ^ { 2 }$; Shift the graph of $f$ to the right $1.3$ units, shrink the graph vertically by a factor of $\frac { 1 } { 5 }$, and shift the graph upward by $2.5$ units. 
B)  Parent function: $f ( x ) = x ^ { 2 }$; Shift the graph of $f$ to the left $1.3$ units, strech the graph vertically by a factor of 5 , and shift the graph downward by $2.5$ units. 
C)  Parent function: $f ( x ) = x ^ { 2 }$; Shift the graph of $f$ to the right $1.3$ units, stretch the graph vertically by a factor of 5 , and shift the graph upward by $2.5$ units. 
D)  Parent function: $f ( x ) = x ^ { 2 }$; Shift the graph of $f$ to the left $1.3$ units, shrink the graph vertically by a factor of $\frac { 1 } { 5 }$, and shift the graph downward by $2.5$ units.

Question 18

Solve the problem.
-The cost to buy tickets online for a dance show is $\$ 60$ per ticket, that is, the cost function is $C ( x ) =$ $60 x$ for $x$ tickets to the show. There is a sales tax of $4.5 \%$ and a processing fee of $\$ 7$ for a group of tickets, that is, $T ( x ) = 1.045 x + 7$ is the total cost for $x$ dollars spent on tickets.
(a) Find $( T \circ C ) ( x )$
(b) Find $( T \circ C ) ( 7 )$ and interpret its meaning in the context of the problem.

Accepted Answer

A)  (a) $( T \circ C ) ( x ) = 62.7 x + 7$; (b) $( T \circ C ) ( 7 ) = 445.9$; The total cost to purchase 7 tickets. 
B)  (a) $( T \circ C ) ( x ) = 62.7 x + 7$; (b) $( T \circ C ) ( 7 ) = 445.9$; The average cost per ticket. 
C)  (a) $( T \circ C ) ( x ) = 62.7 x + 420$; (b) $( T \circ C ) ( 7 ) = 858.9$; The total cost to purchase 7 tickets. 
D)  (a) $( T \circ C ) ( x ) = 62.7 x + 420$; (b) $( T \circ C ) ( 7 ) = 858.9$; The average cost per ticket.

Question 19

Write the domain in interval notation.
-$$m ( x ) = \frac { 5 } { | x | + 1 }$$

Accepted Answer

A)  $( - \infty , - 5 ) \cup ( - 5 , \infty )$ 
B)  $( - \infty , - 1 ) \cup ( - 1,1 ) \cup ( 1 , \infty )$ 
C)  $( - \infty , - 1 ) \cup ( - 1 , \infty )$ 
D)  $( \infty , \infty )$

Question 20

Solve the problem.
-The data in the table shows the number of violent crimes in a certain city in the even years since 2000. $\begin{array}{c|c}
\begin{array}{c}
\text { Years Since } \
\mathbf{2 0 0 0}(\boldsymbol{x})
\end{array} & \begin{array}{c}
\text { Number of } \
\text { Violent Crimes (y) }
\end{array} \
\hline 0 & 19 \
\hline 2 & 33 \
\hline 4 & 43 \
\hline 6 & 46 \
\hline 8 & 57 \
\hline 10 & 63 \
\hline 12 & 78
\end{array}$

Use the data to find the least-squares regression line. Round the slope and $y$-intercept to 1 decimal pl Use the model to approximate the number of violent crimes in the city in $2005 .$

Accepted Answer

A)  $y = 4.1 x + 20.9$; approximately $44.5$ 
B)  $y = 4.4 x + 22.3$; approximately $44.3$ 
C)  $y = 4.8 x + 22.1$; approximately $46.1$ 
D)  $y = 4.5 x + 21.5$; approximately $44.0$ lace.

Exam 2: Functions and Relations

Use the slope-intercept form to write an equation of the line that passes through the given points. Use function notation where y = f(x) . - $( 2 , - 3 )$ and $( - 7 , - 11 )$

Find $\frac { f ( x + h ) - f ( x ) } { h }$ for the given function. - $f ( x ) = \frac { 1 } { x - 4 }$

Determine if the lines defined by the given equations are parallel, perpendicular, or neither. - $\begin{array} { l } - 4 y = 2 x + 5 \\- 4 x = 8 y + 3\end{array}$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The distance from the center of a circle to any point on the circle is called the and is often denoted by r.

Sketch the graph using transformations of a parent function (without a table of values) . - $h ( x ) = \sqrt [ 3 ] { x - 2 }$

Determine which of the given points are solutions to the given equation. - $| x - 3 | - y = 2$ I. $( 1,0 ) \quad$ II. $\left( \frac { 1 } { 4 } , \frac { 3 } { 4 } \right)$ III. $( - 5,10 )$

Evaluate the function for the indicated value, then simplify. - $f ( x ) = x ^ { 2 } + 5 x$ ; find $f ( a + 1 )$ , then simplify as much as possible.

Determine the average rate of change of the function on the given interval. - $f ( x ) = 3 x ^ { 2 } + 3 \text { on } [ 3,5 ]$

Choose the one alternative that best completes the statement or answers the question. Graph the equation and identify the x- and y-intercepts. - $5 y + 1 = 21$

Estimate the x- and y-intercepts from the graph. -

Write an equation of the line satisfying the given conditions. Write the answer in slope-intercept form. -The line passes through the point $( 15 , - 2 )$ and has a slope of $\frac { 2 } { 5 }$ .

Use the given information about a circle to find its equation. -Center $( - 5 , - 4 )$ and diameter 10

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -A function defined by f (x) = mx + b is a function and its graph is a line in a rectangular coordinate system.

Find and simplify f (x + h) . - $f ( x ) = x ^ { 3 } - 5 x + 8$

A function g is given. Identify the parent function. Then use the steps for graphing multiple transformations of functions to list, in order, the transformations applied to the parent function to obtain the graph of g. - $g ( x ) = \frac { 1 } { 5 } ( x + 1.3 ) ^ { 2 } - 2.5$

Write the domain in interval notation. - $m ( x ) = \frac { 5 } { | x | + 1 }$

Exam 2: Functions and Relations

Use the slope-intercept form to write an equation of the line that passes through the given points. Use function notation where y = f(x) . - (2,−3) ( 2 , - 3 ) (2,−3) and (−7,−11) ( - 7 , - 11 ) (−7,−11)

Find f(x+h) −f(x) h\frac { f ( x + h ) - f ( x ) } { h }hf(x+h) −f(x) ​ for the given function. - f(x) =1x−4f ( x ) = \frac { 1 } { x - 4 }f(x) =x−41​

Determine if the lines defined by the given equations are parallel, perpendicular, or neither. - −4y=2x+5−4x=8y+3\begin{array} { l } - 4 y = 2 x + 5 \\- 4 x = 8 y + 3\end{array}−4y=2x+5−4x=8y+3​

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The distance from the center of a circle to any point on the circle is called the and is often denoted by r.

Sketch the graph using transformations of a parent function (without a table of values) . - h(x) =x−23h ( x ) = \sqrt [ 3 ] { x - 2 }h(x) =3x−2​

Determine which of the given points are solutions to the given equation. - ∣x−3∣−y=2| x - 3 | - y = 2∣x−3∣−y=2 I. (1,0) ( 1,0 ) \quad(1,0) II. (14,34) \left( \frac { 1 } { 4 } , \frac { 3 } { 4 } \right) (41​,43​) III. (−5,10) ( - 5,10 ) (−5,10)

Evaluate the function for the indicated value, then simplify. - f(x) =x2+5xf ( x ) = x ^ { 2 } + 5 xf(x) =x2+5x ; find f(a+1) f ( a + 1 ) f(a+1) , then simplify as much as possible.

Determine the average rate of change of the function on the given interval. - f(x) =3x2+3 on [3,5]f ( x ) = 3 x ^ { 2 } + 3 \text { on } [ 3,5 ]f(x) =3x2+3 on [3,5]

Choose the one alternative that best completes the statement or answers the question. Graph the equation and identify the x- and y-intercepts. - 5y+1=215 y + 1 = 215y+1=21