Question 1

If y varies inversely as x, find the inverse variation equation for the situation.
-$y = 90 \text { when } x = 6$

Accepted Answer

A)  $\mathrm { y } = \frac { 540 } { \mathrm { x } }$ 
B)  $y = \frac { x } { 540 }$ 
C)  $y = 15 x$ 
D)  $y = \frac { 1 } { 540 x }$ 
A)  $\mathrm { y } = \frac { 540 } { \mathrm { x } }$ 
B)  $y = \frac { x } { 540 }$ 
C)  $y = 15 x$ 
D)  $y = \frac { 1 } { 540 x }$

Question 2

Graph the function.
-$h(x)=-4|x|$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 3

Find the equation of the line. Write the equation using standard notation.
-Through $( 2 , - 6 )$ and $( 3 , - 11 )$

Accepted Answer

A)  $x + 5 y = 4$ 
B)  $5 x + y = 4$ 
C)  $- 5 x + y = 4$ 
D)  $x - 5 y = 4$ 
A)  $x + 5 y = 4$ 
B)  $5 x + y = 4$ 
C)  $- 5 x + y = 4$ 
D)  $x - 5 y = 4$

Question 4

Solve.
-In a certain city, the cost of a taxi ride is computed as follows: There is a fixed charge of $\$ 2.35$ as soon as you get in the taxi, to which a charge of $\$ 2.05$ per mile is added. Find an equation that can be used to determine the cost of an $x$-mile taxi ride. Use this equation to find the cost of a 8-mile taxi ride.

Accepted Answer

A)  $\$ 18.75$ 
B)  $\$ 18.63$ 
C)  $\$ 19.65$ 
D)  $\$ 18.93$ 
A)  $\$ 18.75$ 
B)  $\$ 18.63$ 
C)  $\$ 19.65$ 
D)  $\$ 18.93$

Question 5

Find the variation equation for the variation statement.
-$z$ varies directly as $x$ and inversely as $y ; z = 5$ when $x = 45$ and $y = 45$

Accepted Answer

A)  $z = \frac { 5 } { x y }$ 
B)  $z = \frac { 5 x } { y }$ 
C)  $z = \frac { x } { 5 y }$ 
D)  $z = 5 x y$ 
A)  $z = \frac { 5 } { x y }$ 
B)  $z = \frac { 5 x } { y }$ 
C)  $z = \frac { x } { 5 y }$ 
D)  $z = 5 x y$

Question 6

If y varies directly as x, find the direct variation equation for the situation.
-$y = 0.3$ when $x = 1.5$

Accepted Answer

A)  $y = x - 1.2$ 
B)  $y = 0.3 x$ 
C)  $y = 5 x$ 
D)  $y = 0.2 x$ 
A)  $y = x - 1.2$ 
B)  $y = 0.3 x$ 
C)  $y = 5 x$ 
D)  $y = 0.2 x$

Question 7

Match the linear function with its graph.
-$f ( x ) = 4 x + 9$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 8

Use the graph of the function to find the value.  
-Find all values of x such that f(x) = -4.

Accepted Answer

A)  -4 
B)  0 
C)  -1, 1 
D)  -2, 2 
A)  -4 
B)  0 
C)  -1, 1 
D)  -2, 2

Question 9

Find an equation of the line with the given slope and containing the given point. Write the equation using function
notation.
-Slope $- \frac { 2 } { 3 } ;$ through $( 3,3 )$

Accepted Answer

A)  $f ( x ) = - \frac { 2 } { 3 } x - 5$ 
B)  $f ( x ) = - \frac { 2 } { 3 } x + 5$ 
C)  $f ( x ) = \frac { 2 } { 3 } x - 5$ 
D)  $f ( x ) = \frac { 2 } { 3 } x + 5$ 
A)  $f ( x ) = - \frac { 2 } { 3 } x - 5$ 
B)  $f ( x ) = - \frac { 2 } { 3 } x + 5$ 
C)  $f ( x ) = \frac { 2 } { 3 } x - 5$ 
D)  $f ( x ) = \frac { 2 } { 3 } x + 5$

Question 10

If y varies inversely as x, find the inverse variation equation for the situation.
-$y = 0.4 \text { when } x = 0.2$

Accepted Answer

A)  $y = \frac { 0.08 } { x }$ 
B)  $y = 2 x$ 
C)  $y = \frac { 12.5 } { x }$ 
D)  $y = 12.5 x$ 
A)  $y = \frac { 0.08 } { x }$ 
B)  $y = 2 x$ 
C)  $y = \frac { 12.5 } { x }$ 
D)  $y = 12.5 x$

Question 11

If y varies directly as x, find the direct variation equation for the situation.
-$y = 2 \text { when } x = \frac { 1 } { 3 }$

Accepted Answer

A)  $y = \frac { 1 } { 2 } x$ 
B)  $y = 6 x$ 
C)  $y = x + \frac { 5 } { 3 }$ 
D)  $y = \frac { 1 } { 6 } x$ 
A)  $y = \frac { 1 } { 2 } x$ 
B)  $y = 6 x$ 
C)  $y = x + \frac { 5 } { 3 }$ 
D)  $y = \frac { 1 } { 6 } x$

Question 12

Solve the problem.
-Sales for a small clothing company can be modeled by the linear function $\mathrm { S } ( \mathrm { x } ) = 3159 \mathrm { x } + 75,939$, where $x$ is the number of years since 2005 and $S ( x )$ is in dollars. Find the sales in 2010 .

Accepted Answer

A)  $\$ 382,854$ 
B)  $\$ 88,575$ 
C)  $\$ 395,490$ 
D)  $\$ 91,734$ 
A)  $\$ 382,854$ 
B)  $\$ 88,575$ 
C)  $\$ 395,490$ 
D)  $\$ 91,734$

Question 13

Fill in the blank with one of the words or phrases listed below. $$\begin{array} { l l l } 
\text { slope-intercept } & \text { directly } & \text { slope } \
\text { jointly } & \text { parallel } & \text { perpendicular } \
\text { function } & \text { inversely } & \text { linear function }
\end{array}$$
-In the equation y = kxz, y varies -----------as x and z.

Accepted Answer

A)  jointly 
B)  directly 
C)  parallel 
D)  inversely 
A)  jointly 
B)  directly 
C)  parallel 
D)  inversely

Question 14

Fill in the blank with one of the words or phrases listed below. $$\begin{array} { l l l } 
\text { slope-intercept } & \text { directly } & \text { slope } \
\text { jointly } & \text { parallel } & \text { perpendicular } \
\text { function } & \text { inversely } & \text { linear function }
\end{array}$$
-In the equation y = kx, y varies ------------as x.

Accepted Answer

A)  inversely 
B)  parallel 
C)  directly 
D)  jointly 
A)  inversely 
B)  parallel 
C)  directly 
D)  jointly

Question 15

Write an equation to describe the variation. Use k for the constant of proportionality.
-$\mathrm { q }$ varies directly as the square of $\mathrm { r }$ and inversely as $\mathrm { s }$.

Accepted Answer

A)  $\mathrm { q } = \frac { \mathrm { kr } ^ { 2 } } { \mathrm {~s} }$ 
B)  $\mathrm { q } = \mathrm { k } + \mathrm { r } ^ { 2 } - \mathrm { s } ^ { 2 }$ 
C)  $q = k ^ { 2 } s$ 
D)  $\mathrm { q } = \frac { \mathrm { ks } } { \mathrm { r } ^ { 2 } }$ 
A)  $\mathrm { q } = \frac { \mathrm { kr } ^ { 2 } } { \mathrm {~s} }$ 
B)  $\mathrm { q } = \mathrm { k } + \mathrm { r } ^ { 2 } - \mathrm { s } ^ { 2 }$ 
C)  $q = k ^ { 2 } s$ 
D)  $\mathrm { q } = \frac { \mathrm { ks } } { \mathrm { r } ^ { 2 } }$

Question 16

Graph the function.
-$g(x)=(x-3)^{2}$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 17

Write an equation to describe the variation. Use k for the constant of proportionality.
-$\mathrm { s }$ varies directly as $\mathrm { m }$

Accepted Answer

A)  $\mathrm { s } = \frac { \mathrm { k } } { \mathrm { m } }$ 
B)  $\mathrm { m } = \frac { \mathrm { k } } { \mathrm { s } }$ 
C)  $\mathrm { s } = \mathrm { km }$ 
D)  $\mathrm { m } = \mathrm { ks }$ 
A)  $\mathrm { s } = \frac { \mathrm { k } } { \mathrm { m } }$ 
B)  $\mathrm { m } = \frac { \mathrm { k } } { \mathrm { s } }$ 
C)  $\mathrm { s } = \mathrm { km }$ 
D)  $\mathrm { m } = \mathrm { ks }$

Question 18

Graph the function. State the domain and range of the function.
-$f(x)=-|x+5|$

Accepted Answer

A)  domain: $( - \infty , \infty )$; range: $( - \infty , 0 ]$
  
B)  domain: $( - \infty , \infty )$; range: $( - \infty , 0 ]$
  
C)  domain: $( - \infty , \infty )$; range: $[ 0 , \infty )$
  
D)  domain: $( - \infty , \infty )$; range: $( \infty , \infty )$
  
A)  domain: $( - \infty , \infty )$; range: $( - \infty , 0 ]$
  
B)  domain: $( - \infty , \infty )$; range: $( - \infty , 0 ]$
  
C)  domain: $( - \infty , \infty )$; range: $[ 0 , \infty )$
  
D)  domain: $( - \infty , \infty )$; range: $( \infty , \infty )$

Question 19

Solve.
-Suppose that y varies directly as the square of x. If x is doubled, what is the effect on y?

Accepted Answer

A)  It's multiplied by 2. 
B)  It's squared. 
C)  It's multiplied by 8. 
D)  It's multiplied by 4. 
A)  It's multiplied by 2. 
B)  It's squared. 
C)  It's multiplied by 8. 
D)  It's multiplied by 4.

Question 20

Solve.
-The distance that an object falls when it is dropped is directly proportional to the square of the amount of time since it was dropped. An object falls $88.2$ meters in 3 seconds. Find the distance the object falls in 5 seconds.

Accepted Answer

A)  245 meters 
B)  147 meters 
C)  15 meters 
D)  49 meters 
A)  245 meters 
B)  147 meters 
C)  15 meters 
D)  49 meters

If y varies inversely as x, find the inverse variation equation for the situation. - $y = 90 \text { when } x = 6$

Graph the function. - $h(x)=-4|x|$

Find the equation of the line. Write the equation using standard notation. -Through $( 2 , - 6 )$ and $( 3 , - 11 )$

Find the variation equation for the variation statement. - $z$ varies directly as $x$ and inversely as $y ; z = 5$ when $x = 45$ and $y = 45$

If y varies directly as x, find the direct variation equation for the situation. - $y = 0.3$ when $x = 1.5$

Match the linear function with its graph. - $f ( x ) = 4 x + 9$

Use the graph of the function to find the value. -Find all values of x such that f(x) = -4.

Find an equation of the line with the given slope and containing the given point. Write the equation using function notation. -Slope $- \frac { 2 } { 3 } ;$ through $( 3,3 )$

If y varies inversely as x, find the inverse variation equation for the situation. - $y = 0.4 \text { when } x = 0.2$

If y varies directly as x, find the direct variation equation for the situation. - $y = 2 \text { when } x = \frac { 1 } { 3 }$

Solve the problem. -Sales for a small clothing company can be modeled by the linear function $\mathrm { S } ( \mathrm { x } ) = 3159 \mathrm { x } + 75,939$ , where $x$ is the number of years since 2005 and $S ( x )$ is in dollars. Find the sales in 2010 .

Fill in the blank with one of the words or phrases listed below. slope-intercept directly slope jointly parallel perpendicular function inversely linear function -In the equation y = kxz, y varies -----------as x and z.

Fill in the blank with one of the words or phrases listed below. slope-intercept directly slope jointly parallel perpendicular function inversely linear function -In the equation y = kx, y varies ------------as x.

Write an equation to describe the variation. Use k for the constant of proportionality. - $\mathrm { q }$ varies directly as the square of $\mathrm { r }$ and inversely as $\mathrm { s }$ .

Graph the function. - $g(x)=(x-3)^{2}$ $Graph the function. - g(x)=(x-3)^{2}$

Write an equation to describe the variation. Use k for the constant of proportionality. - $\mathrm { s }$ varies directly as $\mathrm { m }$

Graph the function. State the domain and range of the function. - $f(x)=-|x+5|$

Solve. -Suppose that y varies directly as the square of x. If x is doubled, what is the effect on y?

Solve. -The distance that an object falls when it is dropped is directly proportional to the square of the amount of time since it was dropped. An object falls $88.2$ meters in 3 seconds. Find the distance the object falls in 5 seconds.

Review of Real Numbers

Equations, Inequalities, and Problem Solving

Graphing

Solving Systems of Linear Equations

Exponents and Polynomials

Factoring Polynomials

Rational Expressions

Inequalities and Absolute Value

Rational Exponents, Radicals, and Complex Numbers

Quadratic Equations and Functions

Exponential and Logarithmic Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 8: More on Functions and Graphs

If y varies inversely as x, find the inverse variation equation for the situation. - y=90 when x=6y = 90 \text { when } x = 6y=90 when x=6

Graph the function. - h(x)=−4∣x∣h(x)=-4|x|h(x)=−4∣x∣

Find the equation of the line. Write the equation using standard notation. -Through (2,−6)( 2 , - 6 )(2,−6) and (3,−11)( 3 , - 11 )(3,−11)

Find the variation equation for the variation statement. - zzz varies directly as xxx and inversely as y;z=5y ; z = 5y;z=5 when x=45x = 45x=45 and y=45y = 45y=45

If y varies directly as x, find the direct variation equation for the situation. - y=0.3y = 0.3y=0.3 when x=1.5x = 1.5x=1.5

Match the linear function with its graph. - f(x)=4x+9f ( x ) = 4 x + 9f(x)=4x+9

Use the graph of the function to find the value. -Find all values of x such that f(x) = -4.

Find an equation of the line with the given slope and containing the given point. Write the equation using function notation. -Slope −23;- \frac { 2 } { 3 } ;−32​; through (3,3)( 3,3 )(3,3)

If y varies inversely as x, find the inverse variation equation for the situation. - y=0.4 when x=0.2y = 0.4 \text { when } x = 0.2y=0.4 when x=0.2

If y varies directly as x, find the direct variation equation for the situation. - y=2 when x=13y = 2 \text { when } x = \frac { 1 } { 3 }y=2 when x=31​

Solve the problem. -Sales for a small clothing company can be modeled by the linear function S(x)=3159x+75,939\mathrm { S } ( \mathrm { x } ) = 3159 \mathrm { x } + 75,939S(x)=3159x+75,939 , where xxx is the number of years since 2005 and S(x)S ( x )S(x) is in dollars. Find the sales in 2010 .

Fill in the blank with one of the words or phrases listed below. slope-intercept directly slope jointly parallel perpendicular function inversely linear function -In the equation y = kxz, y varies -----------as x and z.

Fill in the blank with one of the words or phrases listed below. slope-intercept directly slope jointly parallel perpendicular function inversely linear function -In the equation y = kx, y varies ------------as x.

Write an equation to describe the variation. Use k for the constant of proportionality. - q\mathrm { q }q varies directly as the square of r\mathrm { r }r and inversely as s\mathrm { s }s .

Graph the function. - g(x)=(x−3)2g(x)=(x-3)^{2}g(x)=(x−3)2

Write an equation to describe the variation. Use k for the constant of proportionality. - s\mathrm { s }s varies directly as m\mathrm { m }m

Graph the function. State the domain and range of the function. - f(x)=−∣x+5∣f(x)=-|x+5|f(x)=−∣x+5∣

Solve. -Suppose that y varies directly as the square of x. If x is doubled, what is the effect on y?

Solve. -The distance that an object falls when it is dropped is directly proportional to the square of the amount of time since it was dropped. An object falls 88.288.288.2 meters in 3 seconds. Find the distance the object falls in 5 seconds.

Review of Real Numbers

Equations, Inequalities, and Problem Solving

Graphing

Solving Systems of Linear Equations

Exponents and Polynomials

Factoring Polynomials

Rational Expressions

Inequalities and Absolute Value

Rational Exponents, Radicals, and Complex Numbers

Quadratic Equations and Functions

Exponential and Logarithmic Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

If y varies inversely as x, find the inverse variation equation for the situation. - $y = 90 \text { when } x = 6$

Graph the function. - $h(x)=-4|x|$

Find the equation of the line. Write the equation using standard notation. -Through $( 2 , - 6 )$ and $( 3 , - 11 )$

Find the variation equation for the variation statement. - $z$ varies directly as $x$ and inversely as $y ; z = 5$ when $x = 45$ and $y = 45$

If y varies directly as x, find the direct variation equation for the situation. - $y = 0.3$ when $x = 1.5$

Match the linear function with its graph. - $f ( x ) = 4 x + 9$

Find an equation of the line with the given slope and containing the given point. Write the equation using function notation. -Slope $- \frac { 2 } { 3 } ;$ through $( 3,3 )$

If y varies inversely as x, find the inverse variation equation for the situation. - $y = 0.4 \text { when } x = 0.2$

If y varies directly as x, find the direct variation equation for the situation. - $y = 2 \text { when } x = \frac { 1 } { 3 }$

Solve the problem. -Sales for a small clothing company can be modeled by the linear function $\mathrm { S } ( \mathrm { x } ) = 3159 \mathrm { x } + 75,939$ , where $x$ is the number of years since 2005 and $S ( x )$ is in dollars. Find the sales in 2010 .

Write an equation to describe the variation. Use k for the constant of proportionality. - $\mathrm { q }$ varies directly as the square of $\mathrm { r }$ and inversely as $\mathrm { s }$ .

Graph the function. - $g(x)=(x-3)^{2}$ $Graph the function. - g(x)=(x-3)^{2}$

Write an equation to describe the variation. Use k for the constant of proportionality. - $\mathrm { s }$ varies directly as $\mathrm { m }$

Graph the function. State the domain and range of the function. - $f(x)=-|x+5|$

Solve. -The distance that an object falls when it is dropped is directly proportional to the square of the amount of time since it was dropped. An object falls $88.2$ meters in 3 seconds. Find the distance the object falls in 5 seconds.