Question 1

Determine the quadrant(s) in which (x, y) is located so that the condition(s) is (are) satisfied. ​
X < -8 and y < -6
​

Accepted Answer

A) Quadrant I 
B) Quadrant I and II 
C) Quadrant III 
D) Quadrant II 
E) Quadrant IV 
A) Quadrant I 
B) Quadrant I and II 
C) Quadrant III 
D) Quadrant II 
E) Quadrant IV

Question 2

Identify the following function.   $f ( x ) = 8$

Accepted Answer

A) Constant function 
B) Absolute value function 
C) Square root function 
D) Squaring function 
E) Identity function 
A) Constant function 
B) Absolute value function 
C) Square root function 
D) Squaring function 
E) Identity function

Question 3

Find the coordinates of the point C shown below. ​   ​
​

Accepted Answer

A) (-2, 3) 
B) (3, -2) 
C) (-4, -5) 
D) (-5, -4) 
E) (-5, -2) 
A) (-2, 3) 
B) (3, -2) 
C) (-4, -5) 
D) (-5, -4) 
E) (-5, -2)

Question 4

Use the graph of the function f to create a table of values for the given points.Then create a second table that can be used to find f-1.

Accepted Answer

A)  
$\begin{array}{|l|l|l|l|l|}
\hline x & 1 & 4 & 7 & 8 \
\hline y & 1 & 4 & 7 & 9 \
\hline
\end{array}$

$\begin{array}{|l|l|l|l|l|}
\hline x & 1 & 4 & 7 & 9 \
\hline f^{-1}(x) & 1 & 4 & 7 & 8 \
\hline
\end{array}$ 
B)  
$\begin{array}{|l|l|l|l|l|}
\hline x & 1 & 4 & 7 & 9 \
\hline y & 1 & 4 & 7 & 8 \
\hline
\end{array}$

$\begin{array}{|l|l|l|l|l|}
\hline x & 1 & 4 & 7 & 8 \
\hline f^{-1}(x) & 1 & 4 & 7 & 9 \
\hline
\end{array}$ 
C) 
$\begin{array}{l}
\begin{array} { | l | l | l | l | l | } 
\hline x & 1 & 4 & 7 & 8 \
\hline y & 1 & 4 & 7 & 9 \
\hline
\end{array}\\
\begin{array} { | l | l | l | l | l | } 
\hline x & 1 & 4 & 7 & 9 \
\hline f ^ { - 1 } ( x ) & - 1 & - 4 & - 7 & - 8 \
\hline
\end{array}
\end{array}$ 
D) 
$\begin{array}{l}
\begin{array} { | l | l | l | l | l | } 
\hline x & - 1 & - 4 & - 7 & - 9 \
\hline y & 1 & 4 & 7 & 8 \
\hline
\end{array}\\
\begin{array} { | l | l | l | l | l | } 
\hline x & 1 & 4 & 7 & 8 \
\hline f ^ { - 1 } ( x ) & 1 & 4 & 7 & 9 \
\hline
\end{array}
\end{array}$ 
E) 
$\begin{array}{l}
\begin{array} { | l | l | l | l | l | } 
\hline x & - 1 & - 4 & - 7 & - 9 \
\hline y & 1 & 4 & 7 & 8 \
\hline
\end{array}\\
\begin{array} { | l | l | l | l | l | } 
\hline x & 1 & 4 & 7 & 9 \
\hline f ^ { - 1 } ( x ) & - 1 & - 4 & - 7 & - 8 \
\hline
\end{array}
\end{array}$ 
A)  
$\begin{array}{|l|l|l|l|l|}
\hline x & 1 & 4 & 7 & 8 \
\hline y & 1 & 4 & 7 & 9 \
\hline
\end{array}$

$\begin{array}{|l|l|l|l|l|}
\hline x & 1 & 4 & 7 & 9 \
\hline f^{-1}(x) & 1 & 4 & 7 & 8 \
\hline
\end{array}$ 
B)  
$\begin{array}{|l|l|l|l|l|}
\hline x & 1 & 4 & 7 & 9 \
\hline y & 1 & 4 & 7 & 8 \
\hline
\end{array}$

$\begin{array}{|l|l|l|l|l|}
\hline x & 1 & 4 & 7 & 8 \
\hline f^{-1}(x) & 1 & 4 & 7 & 9 \
\hline
\end{array}$ 
C) 
$\begin{array}{l}
\begin{array} { | l | l | l | l | l | } 
\hline x & 1 & 4 & 7 & 8 \
\hline y & 1 & 4 & 7 & 9 \
\hline
\end{array}\\
\begin{array} { | l | l | l | l | l | } 
\hline x & 1 & 4 & 7 & 9 \
\hline f ^ { - 1 } ( x ) & - 1 & - 4 & - 7 & - 8 \
\hline
\end{array}
\end{array}$ 
D) 
$\begin{array}{l}
\begin{array} { | l | l | l | l | l | } 
\hline x & - 1 & - 4 & - 7 & - 9 \
\hline y & 1 & 4 & 7 & 8 \
\hline
\end{array}\\
\begin{array} { | l | l | l | l | l | } 
\hline x & 1 & 4 & 7 & 8 \
\hline f ^ { - 1 } ( x ) & 1 & 4 & 7 & 9 \
\hline
\end{array}
\end{array}$ 
E) 
$\begin{array}{l}
\begin{array} { | l | l | l | l | l | } 
\hline x & - 1 & - 4 & - 7 & - 9 \
\hline y & 1 & 4 & 7 & 8 \
\hline
\end{array}\\
\begin{array} { | l | l | l | l | l | } 
\hline x & 1 & 4 & 7 & 9 \
\hline f ^ { - 1 } ( x ) & - 1 & - 4 & - 7 & - 8 \
\hline
\end{array}
\end{array}$

Question 5

Find all real values of x such that f(x) = 0. ​
F(x) = 12 - 2x
​

Accepted Answer

A) x = 6 
B) x = 5 
C) x = 7 
D) x = 4 
E) x = 8 
A) x = 6 
B) x = 5 
C) x = 7 
D) x = 4 
E) x = 8

Question 6

The simple interest on an investment is directly proportional to the amount of the investment.By investing $2400 in a certain bond issue, you obtained an interest payment of $111.75 after 1 year.Find a mathematical model that gives the interest I for this bond issue after 1 year in terms of the amount invested P.(Round your answer to three decimal places.)

Accepted Answer

A)  $I = 0.047 P$ 
B)  $I = 268,200 P$ 
C)  $I = 21.477 P$ 
D)  $I = 2400 P$ 
E)  $I = 111.75 P$ 
A)  $I = 0.047 P$ 
B)  $I = 268,200 P$ 
C)  $I = 21.477 P$ 
D)  $I = 2400 P$ 
E)  $I = 111.75 P$

Question 7

Use the graph, which shows the average retail prices of 1 gallon of whole milk from 1996 through 2007. ​   ​
Approximate the percent change in the price of milk from the price in 2000 to the highest price shown in the graph.
​

Accepted Answer

A) About 48% 
B) About 58% 
C) About 43% 
D) About 53% 
E) About 38% 
A) About 48% 
B) About 58% 
C) About 43% 
D) About 53% 
E) About 38%

Question 8

Find the center and radius of the circle, and sketch its graph. 
 $x ^ { 2 } + y ^ { 2 } = 16$

Accepted Answer

A) Centre (0, 0), Radius 16    
B) Centre (0, 0), Radius 4    
C) Centre (0, 0), Radius 4   
D) Centre (0, 0), Radius 16   
E) Centre (0, 0), Radius 4    
A) Centre (0, 0), Radius 16    
B) Centre (0, 0), Radius 4    
C) Centre (0, 0), Radius 4   
D) Centre (0, 0), Radius 16   
E) Centre (0, 0), Radius 4

Question 9

Use the graph of $f ( x ) = x ^ { 2 }$ to write an equation for the function whose graph is shown.

Accepted Answer

A)  $y = x ^ { 2 } + 3$ 
B)  $y = x ^ { 2 } + 4$ 
C)  $y = - x ^ { 2 }$ 
D)  $y = x ^ { 2 } - 3$ 
E)  $y = x ^ { 2 } - 4$ 
A)  $y = x ^ { 2 } + 3$ 
B)  $y = x ^ { 2 } + 4$ 
C)  $y = - x ^ { 2 }$ 
D)  $y = x ^ { 2 } - 3$ 
E)  $y = x ^ { 2 } - 4$

Question 10

Select the graph of the given function and determine the interval(s) for which f(x) ≥ 0. ​
F(x) = 16 - x2
​

Accepted Answer

A) ​   ​[-4, -4] 
B) ​   ​[-4, 4] 
C) ​   ​[-4, -4] 
D) ​   ​[4, -4] 
E) ​   ​[-4, 4] 
A) ​   ​[-4, -4] 
B) ​   ​[-4, 4] 
C) ​   ​[-4, -4] 
D) ​   ​[4, -4] 
E) ​   ​[-4, 4]

Question 11

Find the slope and y-intercept (if possible) of the equation of the line.Select the correct answer for the line.   $3 x - 5 = 0$

Accepted Answer

A)      m is undefined.There is no y-intercept. 
B)     m = -3y-intercept: (0, 5) 
C)     m is undefined.There is no y-intercept. 
D)    m = -5y-intercept: (0, 3) 
E)       m is undefined.There is no y-intercept. 
A)      m is undefined.There is no y-intercept. 
B)     m = -3y-intercept: (0, 5) 
C)     m is undefined.There is no y-intercept. 
D)    m = -5y-intercept: (0, 3) 
E)       m is undefined.There is no y-intercept.

Question 12

Determine whether the function has an inverse function.If it does, find the inverse function. 
 $f ( x ) = \left\{ \begin{array} { l } 
x + 2 , x < 0 \
2 - x , x \geq 0
\end{array} \right.$

Accepted Answer

A)  $f ^ { - 1 } ( x ) = \left\{ \begin{array} { l } 
2 + x , x \geq 0 \
x - 2 , x < 0
\end{array} \right.$ 
B)  $f ^ { - 1 } ( x ) = \left\{ \begin{array} { l } 
2 + x , x \geq 0 \
x - 2 , x < 0
\end{array} \right.$. 
C)  $f ^ { - 1 } ( x ) = \left\{ \begin{array} { l } 
x - 2 , x \geq 0 \
2 + x , x < 0
\end{array} \right.$ 
D)  $f ^ { - 1 } ( x ) = \left\{ \begin{array} { l } 
x + 2 , x \geq 0 \
2 - x , x < 0
\end{array} \right.$ 
E) No inverse 
A)  $f ^ { - 1 } ( x ) = \left\{ \begin{array} { l } 
2 + x , x \geq 0 \
x - 2 , x < 0
\end{array} \right.$ 
B)  $f ^ { - 1 } ( x ) = \left\{ \begin{array} { l } 
2 + x , x \geq 0 \
x - 2 , x < 0
\end{array} \right.$. 
C)  $f ^ { - 1 } ( x ) = \left\{ \begin{array} { l } 
x - 2 , x \geq 0 \
2 + x , x < 0
\end{array} \right.$ 
D)  $f ^ { - 1 } ( x ) = \left\{ \begin{array} { l } 
x + 2 , x \geq 0 \
2 - x , x < 0
\end{array} \right.$ 
E) No inverse

Question 13

Write the equation of the line that passes through the point P(0, 0) and is parallel to the line y = 8x - 7. ​

Accepted Answer

A) x = 8y 
B) y = 7x +8 
C) y = -7x 
D) y = 8x 
E) y = 7x 
A) x = 8y 
B) y = 7x +8 
C) y = -7x 
D) y = 8x 
E) y = 7x

Question 14

Select the graph of f and f-1 on the same set of coordinate axes. 
 $f ( x ) = \frac { 3 } { x }$

Accepted Answer

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

Question 15

​Plot the points in the Cartesian plane. ​
(2, 6), (2.5, 6), (3, -6), (-6, 4.5)
​

Accepted Answer

A) ​   
B) ​   
C) ​   
D) ​   
E) ​   
A) ​   
B) ​   
C) ​   
D) ​   
E) ​

Question 16

Use the graph of $f ( x ) = | x |$ to write an equation for the function whose graph is shown.

Accepted Answer

A)  $y = - | x + 5 | - 1$ 
B)  $y = | x + 5 | + 1$ 
C)  $y = - | x - 5 | + 1$ 
D)  $y = - | x - 5 | - 1$ 
E)  $y = | x - 5 | - 1$ 
A)  $y = - | x + 5 | - 1$ 
B)  $y = | x + 5 | + 1$ 
C)  $y = - | x - 5 | + 1$ 
D)  $y = - | x - 5 | - 1$ 
E)  $y = | x - 5 | - 1$

Question 17

Graphically estimate the x- and y-intercepts of the graph. ​
Y = |x + 3|
​   ​

Accepted Answer

A) x-intercept: (-3, 0)y-intercept: (0, 3) 
B) x-intercept: (0, -3)y-intercept: (3, 0) 
C) x-intercept: (0, -3)y-intercept: (0, 3) 
D) x-intercept: (3, 0)y-intercept: (3, 0) 
E) x-intercept: (0, 3)y-intercept: (3, 0) 
A) x-intercept: (-3, 0)y-intercept: (0, 3) 
B) x-intercept: (0, -3)y-intercept: (3, 0) 
C) x-intercept: (0, -3)y-intercept: (0, 3) 
D) x-intercept: (3, 0)y-intercept: (3, 0) 
E) x-intercept: (0, 3)y-intercept: (3, 0)

Question 18

Select the correct graph of the given function. 
 $f ( x ) = 2 - | x |$

Accepted Answer

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

Question 19

Find (fg)(x).   $f ( x ) = x ^ { 2 } , g ( x ) = 7 x - 7$

Accepted Answer

A)  $7 x ^ { 3 } + 7 x ^ { 2 }$ 
B)  $7 x ^ { 3 } - 7 x ^ { 2 }$ 
C)  $7 x ^ { 2 } - 7 x ^ { 3 }$ 
D)  $7 x ^ { 2 } + 7 x ^ { 3 }$ 
E)  $7 x - 7 x ^ { 2 }$ 
A)  $7 x ^ { 3 } + 7 x ^ { 2 }$ 
B)  $7 x ^ { 3 } - 7 x ^ { 2 }$ 
C)  $7 x ^ { 2 } - 7 x ^ { 3 }$ 
D)  $7 x ^ { 2 } + 7 x ^ { 3 }$ 
E)  $7 x - 7 x ^ { 2 }$

Question 20

Use the functions given by $f ( x ) = \frac { 1 } { 125 } x - 1$ and g(x) = x3 to find (f º g)-1.

Accepted Answer

A)  $5 \sqrt [ 3 ] { x - 1 }$ 
B)  $125 \sqrt [ 3 ] { x - 1 }$ 
C)  $5 \sqrt [ 3 ] { x + 1 }$ 
D)  $125 \sqrt [ 3 ] { x + 1 }$ 
E)  $5 \sqrt { x + 1 }$ 
A)  $5 \sqrt [ 3 ] { x - 1 }$ 
B)  $125 \sqrt [ 3 ] { x - 1 }$ 
C)  $5 \sqrt [ 3 ] { x + 1 }$ 
D)  $125 \sqrt [ 3 ] { x + 1 }$ 
E)  $5 \sqrt { x + 1 }$

Determine the quadrant(s) in which (x, y) is located so that the condition(s) is (are) satisfied. X < -8 and y < -6

Identify the following function. $f ( x ) = 8$

Find the coordinates of the point C shown below.

Use the graph of the function f to create a table of values for the given points.Then create a second table that can be used to find f^-1.

Find all real values of x such that f(x) = 0. F(x) = 12 - 2x

Use the graph, which shows the average retail prices of 1 gallon of whole milk from 1996 through 2007. Approximate the percent change in the price of milk from the price in 2000 to the highest price shown in the graph.

Find the center and radius of the circle, and sketch its graph. $x ^ { 2 } + y ^ { 2 } = 16$

Use the graph of $f ( x ) = x ^ { 2 }$ to write an equation for the function whose graph is shown. $Use the graph of f ( x ) = x ^ { 2 } to write an equation for the function whose graph is shown.$

Select the graph of the given function and determine the interval(s) for which f(x) ≥ 0. F(x) = 16 - x²

Find the slope and y-intercept (if possible) of the equation of the line.Select the correct answer for the line. $3 x - 5 = 0$

Determine whether the function has an inverse function.If it does, find the inverse function. $f ( x ) = \left\{ \begin{array} { l } x + 2 , x < 0 \\2 - x , x \geq 0\end{array} \right.$

Write the equation of the line that passes through the point P(0, 0) and is parallel to the line y = 8x - 7.

Select the graph of f and f^-1 on the same set of coordinate axes. $f ( x ) = \frac { 3 } { x }$

Plot the points in the Cartesian plane. (2, 6), (2.5, 6), (3, -6), (-6, 4.5)

Use the graph of $f ( x ) = | x |$ to write an equation for the function whose graph is shown.

Graphically estimate the x- and y-intercepts of the graph. Y = |x + 3|

Select the correct graph of the given function. $f ( x ) = 2 - | x |$

Find (fg)(x). $f ( x ) = x ^ { 2 } , g ( x ) = 7 x - 7$

Use the functions given by $f ( x ) = \frac { 1 } { 125 } x - 1$ and g(x) = x³ to find (f _º g)^-1.

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Additional Topics In Trigonometery

Systems Of Equations and Inequalities

Matrices and Determinants

Sequences Series and Probability

Topics In Analytic Geometry

Analytic Geometry In Three Dimensions

Limits and An Introduction To Calculus

Filters

Exam 1: Functions and Their Graphs

Determine the quadrant(s) in which (x, y) is located so that the condition(s) is (are) satisfied. ​ X < -8 and y < -6 ​

Identify the following function. f(x)=8f ( x ) = 8f(x)=8

Find the coordinates of the point C shown below. ​ ​ ​

Use the graph of the function f to create a table of values for the given points.Then create a second table that can be used to find f-1.

Find all real values of x such that f(x) = 0. ​ F(x) = 12 - 2x ​

Use the graph, which shows the average retail prices of 1 gallon of whole milk from 1996 through 2007. ​ ​ Approximate the percent change in the price of milk from the price in 2000 to the highest price shown in the graph. ​

Find the center and radius of the circle, and sketch its graph. x2+y2=16x ^ { 2 } + y ^ { 2 } = 16x2+y2=16

Use the graph of f(x)=x2f ( x ) = x ^ { 2 }f(x)=x2 to write an equation for the function whose graph is shown.

Select the graph of the given function and determine the interval(s) for which f(x) ≥ 0. ​ F(x) = 16 - x2 ​

Find the slope and y-intercept (if possible) of the equation of the line.Select the correct answer for the line. 3x−5=03 x - 5 = 03x−5=0

Determine whether the function has an inverse function.If it does, find the inverse function. f(x)={x+2,x<02−x,x≥0f ( x ) = \left\{ \begin{array} { l } x + 2 , x < 0 \\2 - x , x \geq 0\end{array} \right.f(x)={x+2,x<02−x,x≥0​

Write the equation of the line that passes through the point P(0, 0) and is parallel to the line y = 8x - 7. ​

Select the graph of f and f-1 on the same set of coordinate axes. f(x)=3xf ( x ) = \frac { 3 } { x }f(x)=x3​

​Plot the points in the Cartesian plane. ​ (2, 6), (2.5, 6), (3, -6), (-6, 4.5) ​

Use the graph of f(x)=∣x∣f ( x ) = | x |f(x)=∣x∣ to write an equation for the function whose graph is shown.

Graphically estimate the x- and y-intercepts of the graph. ​ Y = |x + 3| ​ ​

Select the correct graph of the given function. f(x)=2−∣x∣f ( x ) = 2 - | x |f(x)=2−∣x∣

Find (fg)(x). f(x)=x2,g(x)=7x−7f ( x ) = x ^ { 2 } , g ( x ) = 7 x - 7f(x)=x2,g(x)=7x−7

Use the functions given by f(x)=1125x−1f ( x ) = \frac { 1 } { 125 } x - 1f(x)=1251​x−1 and g(x) = x3 to find (f º g)-1.

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Additional Topics In Trigonometery

Systems Of Equations and Inequalities

Matrices and Determinants

Sequences Series and Probability

Topics In Analytic Geometry

Analytic Geometry In Three Dimensions

Limits and An Introduction To Calculus

Filters

Determine the quadrant(s) in which (x, y) is located so that the condition(s) is (are) satisfied. X < -8 and y < -6

Identify the following function. $f ( x ) = 8$

Find the coordinates of the point C shown below.

Use the graph of the function f to create a table of values for the given points.Then create a second table that can be used to find f^-1.

Find all real values of x such that f(x) = 0. F(x) = 12 - 2x

Use the graph, which shows the average retail prices of 1 gallon of whole milk from 1996 through 2007. Approximate the percent change in the price of milk from the price in 2000 to the highest price shown in the graph.

Find the center and radius of the circle, and sketch its graph. $x ^ { 2 } + y ^ { 2 } = 16$

Use the graph of $f ( x ) = x ^ { 2 }$ to write an equation for the function whose graph is shown. $Use the graph of f ( x ) = x ^ { 2 } to write an equation for the function whose graph is shown.$

Select the graph of the given function and determine the interval(s) for which f(x) ≥ 0. F(x) = 16 - x²

Find the slope and y-intercept (if possible) of the equation of the line.Select the correct answer for the line. $3 x - 5 = 0$

Determine whether the function has an inverse function.If it does, find the inverse function. $f ( x ) = \left\{ \begin{array} { l } x + 2 , x < 0 \\2 - x , x \geq 0\end{array} \right.$

Write the equation of the line that passes through the point P(0, 0) and is parallel to the line y = 8x - 7.

Select the graph of f and f^-1 on the same set of coordinate axes. $f ( x ) = \frac { 3 } { x }$

Plot the points in the Cartesian plane. (2, 6), (2.5, 6), (3, -6), (-6, 4.5)

Use the graph of $f ( x ) = | x |$ to write an equation for the function whose graph is shown.

Graphically estimate the x- and y-intercepts of the graph. Y = |x + 3|

Select the correct graph of the given function. $f ( x ) = 2 - | x |$

Find (fg)(x). $f ( x ) = x ^ { 2 } , g ( x ) = 7 x - 7$

Use the functions given by $f ( x ) = \frac { 1 } { 125 } x - 1$ and g(x) = x³ to find (f _º g)^-1.