Question 1

Write an equation to describe the variation. Use k for the constant of proportionality.
-$x$ varies jointly as $y$ and $z$.

Accepted Answer

A)  $x = k y z$ 
B)  $x = k + y + z$ 
C)  $x y z = k$ 
D)  $x + y + z = k$ 
A)  $x = k y z$ 
B)  $x = k + y + z$ 
C)  $x y z = k$ 
D)  $x + y + z = k$

Question 2

Solve.
-While traveling in a car, the centrifugal force a passenger experiences as the car drives in a circle varies jointly as the mass of the passenger and the square of the speed of the car. If the a passenger Experiences a force of 324 newtons when the car is moving at a speed of 60 kilometers per hour and
The passenger has a mass of 100 kilograms, find the force a passenger experiences when the car is Moving at 70 kilometers per hour and the passenger has a mass of 80 kilograms.

Accepted Answer

A)  352.8 newtons 
B)  313.6 newtons 
C)  392 newtons 
D)  441 newtons 
A)  352.8 newtons 
B)  313.6 newtons 
C)  392 newtons 
D)  441 newtons

Question 3

Solve.
-In 2010 a certain county recovered 27% of its municipal wastes through recycling, up from 17% in 2005. Find a linear equation that fits this data. Use this equation to predict the percentage recycled
In 2021.

Accepted Answer

A)  45.4% 
B)  47.1% 
C)  50.7% 
D)  49% 
A)  45.4% 
B)  47.1% 
C)  50.7% 
D)  49%

Question 4

Graph the piecewise defined function.
-$f ( x ) = \left\{ \begin{array} { l l } 
1 & \text { if } x \leq - 1 \
- 5 + x & \text { if } x > - 1 \
\end{array} \right.$

Accepted Answer

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

Question 5

Graph the linear function.
-$f(x)=\frac{7}{3} x+7$

Accepted Answer

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

Question 6

Graph the function.
-$f(x)=-|x|$

Accepted Answer

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

Question 7

Find the equation of the line. Write the equation using standard notation.
-Through $( - 9 , - 1 )$; parallel to $x = 8$

Accepted Answer

A)  $\mathrm { y } = - 1$ 
B)  $x = - 1$ 
C)  $x = - 9$ 
D)  $y = - 9$ 
A)  $\mathrm { y } = - 1$ 
B)  $x = - 1$ 
C)  $x = - 9$ 
D)  $y = - 9$

Question 8

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

Accepted Answer

A)  $\mathrm { p } = \mathrm { kq } ^ { 2 } \mathrm { r } ^ { 2 }$ 
B)  $p q ^ { 2 } r ^ { 2 } = k$ 
C)  $p + q ^ { 2 } + r ^ { 2 } = k$ 
D)  $p = k + q ^ { 2 } + r ^ { 2 }$ 
A)  $\mathrm { p } = \mathrm { kq } ^ { 2 } \mathrm { r } ^ { 2 }$ 
B)  $p q ^ { 2 } r ^ { 2 } = k$ 
C)  $p + q ^ { 2 } + r ^ { 2 } = k$ 
D)  $p = k + q ^ { 2 } + r ^ { 2 }$

Question 9

If y varies inversely as x, find the inverse variation equation for the situation.
-$y = 45 \text { when } x = \frac { 1 } { 9 }$

Accepted Answer

A)  $y = \frac { x } { 5 }$ 
B)  $y = \frac { 5 } { x }$ 
C)  $y = \frac { 1 } { 5 x }$ 
D)  $y = 405 x$ 
A)  $y = \frac { x } { 5 }$ 
B)  $y = \frac { 5 } { x }$ 
C)  $y = \frac { 1 } { 5 x }$ 
D)  $y = 405 x$

Question 10

Find an equation of the line. Write the equation using function notation.
-$\left( 1 , \frac { 4 } { 9 } \right) , \left( 9 , \frac { 4 } { 3 } \right)$

Accepted Answer

A)  $y = \frac { 1 } { 9 } x + \frac { 1 } { 3 }$ 
B)  $y = 9 x - \frac { 77 } { 9 }$ 
C)  $f(x) = \frac { 1 } { 9 } x + \frac { 1 } { 3 }$ 
D)  f(x)=9x-3 
A)  $y = \frac { 1 } { 9 } x + \frac { 1 } { 3 }$ 
B)  $y = 9 x - \frac { 77 } { 9 }$ 
C)  $f(x) = \frac { 1 } { 9 } x + \frac { 1 } { 3 }$ 
D)  f(x)=9x-3

Question 11

Fill in the blank with one of the words or phrases listed below. $$\begin{array} { l l l } 
\text { slope-intercept } & \text { directly } & \text { slope } \
\text { jointly } & \text { parallel } & \text { perpendicular } \
\text { function } & \text { inversely } & \text { linear function }
\end{array}$$
-A(n)_______ is a function that can be written in the form $f ( x ) = m x + b$.

Accepted Answer

A)  perpendicular 
B)  linear function 
C)  parallel 
D)  slope-intercept 
A)  perpendicular 
B)  linear function 
C)  parallel 
D)  slope-intercept

Question 12

Solve.
-The amount of water used to take a shower is directly proportional to the amount of time that the shower is in use. A shower lasting 20 minutes requires 16 gallons of water. Find the amount of Water used in a shower lasting 4 minutes.

Accepted Answer

A)  3.2 gallons 
B)  4 gallons 
C)  80 gallons 
D)  2.4 gallons 
A)  3.2 gallons 
B)  4 gallons 
C)  80 gallons 
D)  2.4 gallons

Question 13

Find the equation of the line. Write the equation using standard notation.
-Through $( 2,2 )$; perpendicular to the line $2 x - 7 y = 2$

Accepted Answer

A)  $2 x + 7 y = 18$ 
B)  $7 x - 2 y = 18$ 
C)  $2 x - 7 y = 18$ 
D)  $7 x + 2 y = 18$ 
A)  $2 x + 7 y = 18$ 
B)  $7 x - 2 y = 18$ 
C)  $2 x - 7 y = 18$ 
D)  $7 x + 2 y = 18$

Question 14

Write an equation of the line using function notation.
-Horizontal; through $( 0 , - 4 )$

Accepted Answer

A)  $x = - 4$ 
B)  $x = 0$ 
C)  $f ( x ) = 0$ 
D)  $f ( x ) = - 4$ 
A)  $x = - 4$ 
B)  $x = 0$ 
C)  $f ( x ) = 0$ 
D)  $f ( x ) = - 4$

Question 15

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

Accepted Answer

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

Question 16

Graph the piecewise defined function.
-$f(x)=\left\{\begin{array}{rr}
3 x-1 & \text { if } x \leq 3 \
-x & \text { if } x>3
\end{array}\right.$

Accepted Answer

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

Question 17

Solve.
-When making a telephone call using a calling card, a call lasting 4 minutes costs $\$ 2.10$. A call lasting 11 minutes costs $\$ 4.90$. Let $y$ be the cost of making a call lasting $x$ minutes using a calling card. Write a linear equation that relates cost $y$ to time $x$.

Accepted Answer

A)  $y = 0.4 x - 6.1$ 
B)  $y = 0.4 x + 0.5$ 
C)  $y = - 0.4 x + 3.7$ 
D)  $y = \frac { 5 } { 2 } x - \frac { 79 } { 10 }$ 
A)  $y = 0.4 x - 6.1$ 
B)  $y = 0.4 x + 0.5$ 
C)  $y = - 0.4 x + 3.7$ 
D)  $y = \frac { 5 } { 2 } x - \frac { 79 } { 10 }$

Question 18

Use the graph of the function to find the value.  
-Find all values of x such that f(x) = 0.

Accepted Answer

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

Question 19

Find the square root.
-$\sqrt { 16 }$

Accepted Answer

A)  2 
B)  16 
C)  8 
D)  4 
A)  2 
B)  16 
C)  8 
D)  4

Question 20

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

Accepted Answer

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

Write an equation to describe the variation. Use k for the constant of proportionality. - $x$ varies jointly as $y$ and $z$ .

Solve. -In 2010 a certain county recovered 27% of its municipal wastes through recycling, up from 17% in 2005. Find a linear equation that fits this data. Use this equation to predict the percentage recycled In 2021.

Graph the linear function. - $f(x)=\frac{7}{3} x+7$ $Graph the linear function. - f(x)=\frac{7}{3} x+7$

Graph the function. - $f(x)=-|x|$

Find the equation of the line. Write the equation using standard notation. -Through $( - 9 , - 1 )$ ; parallel to $x = 8$

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

If y varies inversely as x, find the inverse variation equation for the situation. - $y = 45 \text { when } x = \frac { 1 } { 9 }$

Find an equation of the line. Write the equation using function notation. - $\left( 1 , \frac { 4 } { 9 } \right) , \left( 9 , \frac { 4 } { 3 } \right)$

Fill in the blank with one of the words or phrases listed below. slope-intercept directly slope jointly parallel perpendicular function inversely linear function -A(n)_______ is a function that can be written in the form $f ( x ) = m x + b$ .

Solve. -The amount of water used to take a shower is directly proportional to the amount of time that the shower is in use. A shower lasting 20 minutes requires 16 gallons of water. Find the amount of Water used in a shower lasting 4 minutes.

Find the equation of the line. Write the equation using standard notation. -Through $( 2,2 )$ ; perpendicular to the line $2 x - 7 y = 2$

Write an equation of the line using function notation. -Horizontal; through $( 0 , - 4 )$

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

Graph the piecewise defined function. - $f(x)=\left\{\begin{array}{rr}3 x-1 & \text { if } x \leq 3 \\-x & \text { if } x>3\end{array}\right.$ $Graph the piecewise defined function. - f(x)=\left\{\begin{array}{rr} 3 x-1 & \text { if } x \leq 3 \\ -x & \text { if } x>3 \end{array}\right.$

Solve. -When making a telephone call using a calling card, a call lasting 4 minutes costs $\$ 2.10$ . A call lasting 11 minutes costs $\$ 4.90$ . Let $y$ be the cost of making a call lasting $x$ minutes using a calling card. Write a linear equation that relates cost $y$ to time $x$ .

Use the graph of the function to find the value. -Find all values of x such that f(x) = 0.

Find the square root. - $\sqrt { 16 }$

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

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

Write an equation to describe the variation. Use k for the constant of proportionality. - xxx varies jointly as yyy and zzz .

Solve. -In 2010 a certain county recovered 27% of its municipal wastes through recycling, up from 17% in 2005. Find a linear equation that fits this data. Use this equation to predict the percentage recycled In 2021.

Graph the piecewise defined function. - f(x)={1 if x≤−1−5+x if x>−1f ( x ) = \left\{ \begin{array} { l l } 1 & \text { if } x \leq - 1 \\- 5 + x & \text { if } x > - 1 \\\end{array} \right.f(x)={1−5+x​ if x≤−1 if x>−1​

Graph the linear function. - f(x)=73x+7f(x)=\frac{7}{3} x+7f(x)=37​x+7

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

Find the equation of the line. Write the equation using standard notation. -Through (−9,−1)( - 9 , - 1 )(−9,−1) ; parallel to x=8x = 8x=8

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

If y varies inversely as x, find the inverse variation equation for the situation. - y=45 when x=19y = 45 \text { when } x = \frac { 1 } { 9 }y=45 when x=91​

Find an equation of the line. Write the equation using function notation. - (1,49),(9,43)\left( 1 , \frac { 4 } { 9 } \right) , \left( 9 , \frac { 4 } { 3 } \right)(1,94​),(9,34​)

Fill in the blank with one of the words or phrases listed below. slope-intercept directly slope jointly parallel perpendicular function inversely linear function -A(n)_______ is a function that can be written in the form f(x)=mx+bf ( x ) = m x + bf(x)=mx+b .

Solve. -The amount of water used to take a shower is directly proportional to the amount of time that the shower is in use. A shower lasting 20 minutes requires 16 gallons of water. Find the amount of Water used in a shower lasting 4 minutes.

Find the equation of the line. Write the equation using standard notation. -Through (2,2)( 2,2 )(2,2) ; perpendicular to the line 2x−7y=22 x - 7 y = 22x−7y=2

Write an equation of the line using function notation. -Horizontal; through (0,−4)( 0 , - 4 )(0,−4)

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

Graph the piecewise defined function. - f(x)={3x−1 if x≤3−x if x>3f(x)=\left\{\begin{array}{rr}3 x-1 & \text { if } x \leq 3 \\-x & \text { if } x>3\end{array}\right.f(x)={3x−1−x​ if x≤3 if x>3​

Use the graph of the function to find the value. -Find all values of x such that f(x) = 0.

Find the square root. - 16\sqrt { 16 }16​

Graph the function. - f(x)=x2−2f ( x ) = x ^ { 2 } - 2f(x)=x2−2

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

Write an equation to describe the variation. Use k for the constant of proportionality. - $x$ varies jointly as $y$ and $z$ .

Graph the linear function. - $f(x)=\frac{7}{3} x+7$ $Graph the linear function. - f(x)=\frac{7}{3} x+7$

Graph the function. - $f(x)=-|x|$

Find the equation of the line. Write the equation using standard notation. -Through $( - 9 , - 1 )$ ; parallel to $x = 8$

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

If y varies inversely as x, find the inverse variation equation for the situation. - $y = 45 \text { when } x = \frac { 1 } { 9 }$

Find an equation of the line. Write the equation using function notation. - $\left( 1 , \frac { 4 } { 9 } \right) , \left( 9 , \frac { 4 } { 3 } \right)$

Fill in the blank with one of the words or phrases listed below. slope-intercept directly slope jointly parallel perpendicular function inversely linear function -A(n)_______ is a function that can be written in the form $f ( x ) = m x + b$ .

Find the equation of the line. Write the equation using standard notation. -Through $( 2,2 )$ ; perpendicular to the line $2 x - 7 y = 2$

Write an equation of the line using function notation. -Horizontal; through $( 0 , - 4 )$

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

Graph the piecewise defined function. - $f(x)=\left\{\begin{array}{rr}3 x-1 & \text { if } x \leq 3 \\-x & \text { if } x>3\end{array}\right.$ $Graph the piecewise defined function. - f(x)=\left\{\begin{array}{rr} 3 x-1 & \text { if } x \leq 3 \\ -x & \text { if } x>3 \end{array}\right.$

Find the square root. - $\sqrt { 16 }$

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