Question 1

Does the table describe a function?
$\begin{array}{|c|c|c|c|c|c|}
\hline \text { Input value } & -6 & -3 & 0 & 3 & 6 \
\hline \text { Output value } & 11 & 11 & 11 & 11 & 11 \
\hline
\end{array}$

Accepted Answer

A)  $y \mathrm { es }$ 
B)  no 
A)  $y \mathrm { es }$ 
B)  no

Question 2

Find the slope and y-intercept of the equation of the line. $$y = - 2 x + 3$$

Accepted Answer

A)  slope: $- \frac { 1 } { 2 } ; y$-intercept: 3 
B)  slope: $\frac { 1 } { 3 } ; y$-intercept: $- 2$ 
C)  slope: $- 2 ; y$-intercept: 3 
D)  slope: $3 ; y$-intercept: $- 2$ 
E)  slope: $- 2 ; y$-intercept: $- 3$ 
A)  slope: $- \frac { 1 } { 2 } ; y$-intercept: 3 
B)  slope: $\frac { 1 } { 3 } ; y$-intercept: $- 2$ 
C)  slope: $- 2 ; y$-intercept: 3 
D)  slope: $3 ; y$-intercept: $- 2$ 
E)  slope: $- 2 ; y$-intercept: $- 3$

Question 3

Hooke's Law states that the force $F$ required to compress or stretch a spring (within its elastic limits) is proportional to the distance $d$ that the spring is compressed or stretched from its original length. That is, $F = k d$, where $k$ is the measure of the stiffness of the spring and is called the spring constant. The table below shows the elongation $d$ in centimeters of a spring when a force of $F$ kilograms is applied. 
$\begin{array}{|c|c|}
\hline \text { Force, } \boldsymbol{F} & \text { Elongation, } \boldsymbol{d} \
\hline 20 & 3.5 \
\hline 40 & 6.3 \
\hline 60 & 10.0 \
\hline 80 & 13.3 \
\hline 100 & 16.5 \
\hline
\end{array}$

Find the equation of the line that seems to best fit the data.

Accepted Answer

A)  $F = 12.098 d$ 
B)  $F = 3.024 d$ 
C)  $F = 6.049 d$ 
D)  $F = 4.537 d$ 
E)  $\quad F = 7.561 d$ 
A)  $F = 12.098 d$ 
B)  $F = 3.024 d$ 
C)  $F = 6.049 d$ 
D)  $F = 4.537 d$ 
E)  $\quad F = 7.561 d$

Question 4

Use function notation to write $g$ in terms of $f ( x ) = x ^ { 3 }$.
$$g ( x ) = - \frac { 1 } { 4 } ( x + 9 ) ^ { 3 }$$

Accepted Answer

A)  $g ( x ) = - \frac { 1 } { 4 } [ f ( x ) ] ^ { 3 } + 9$ 
B)  $g ( x ) = - \frac { 1 } { 4 } [ f ( x ) + 9 ]$ 
C)  $\quad g ( x ) = - [ f ( x ) ] ^ { 3 } + \frac { 729 } { 4 }$ 
D)  $\quad g ( x ) = - \frac { 1 } { 4 } [ f ( x ) ] ^ { 3 } + 729$ 
E)  $g ( x ) = - \frac { 1 } { 4 } [ f ( x + 9 ) ]$ 
A)  $g ( x ) = - \frac { 1 } { 4 } [ f ( x ) ] ^ { 3 } + 9$ 
B)  $g ( x ) = - \frac { 1 } { 4 } [ f ( x ) + 9 ]$ 
C)  $\quad g ( x ) = - [ f ( x ) ] ^ { 3 } + \frac { 729 } { 4 }$ 
D)  $\quad g ( x ) = - \frac { 1 } { 4 } [ f ( x ) ] ^ { 3 } + 729$ 
E)  $g ( x ) = - \frac { 1 } { 4 } [ f ( x + 9 ) ]$

Question 5

Find the domain of the function. $g ( x ) = \sqrt { 25 - x ^ { 2 } }$

Accepted Answer

A)  $- 5 \leq x \leq 5$ 
B)  $x \leq - 5$ or $x \geq 5$ 
C)  $x \geq 0$ 
D)  $x \leq 5$ 
E)  all real numbers 
A)  $- 5 \leq x \leq 5$ 
B)  $x \leq - 5$ or $x \geq 5$ 
C)  $x \geq 0$ 
D)  $x \leq 5$ 
E)  all real numbers

Question 6

Find the domain of the function. $f ( y ) = \sqrt { 9 - y ^ { 2 } }$

Accepted Answer

A)  $- 3 \leq y \leq 3$ 
B)  $y \leq - 3$ or $y \geq 3$ 
C)  $y \geq 0$ 
D)  $y \leq 3$ 
E)  all real numbers 
A)  $- 3 \leq y \leq 3$ 
B)  $y \leq - 3$ or $y \geq 3$ 
C)  $y \geq 0$ 
D)  $y \leq 3$ 
E)  all real numbers

Question 7

Find the domain of the function. $$f ( t ) = \sqrt { 64 - t ^ { 2 } }$$

Accepted Answer

A)  $- 8 \leq t \leq 8$ 
B)  $t \leq - 8$ or $t \geq 8$ 
C)  $t \geq 0$ 
D)  $t \leq 8$ 
E)  all real numbers 
A)  $- 8 \leq t \leq 8$ 
B)  $t \leq - 8$ or $t \geq 8$ 
C)  $t \geq 0$ 
D)  $t \leq 8$ 
E)  all real numbers

Question 8

Find $g \circ f$.

Accepted Answer

A)  $( g \circ f ) ( x ) = x ^ { 2 } + 2$ 
B)  $( g \circ f ) ( x ) = x ^ { 2 } - 4$ 
C)  $( g \circ f ) ( x ) = x ^ { 2 } + 4$ 
D)  $( g \circ f ) ( x ) = x ^ { 2 } + 2 x + 4$ 
E)  $\quad ( g \circ f ) ( x ) = x ^ { 2 } + 4 x + 4$ 
A)  $( g \circ f ) ( x ) = x ^ { 2 } + 2$ 
B)  $( g \circ f ) ( x ) = x ^ { 2 } - 4$ 
C)  $( g \circ f ) ( x ) = x ^ { 2 } + 4$ 
D)  $( g \circ f ) ( x ) = x ^ { 2 } + 2 x + 4$ 
E)  $\quad ( g \circ f ) ( x ) = x ^ { 2 } + 4 x + 4$

Question 9

Restrict the domain of the following function $f$ so that the function is one-to-one and has an inverse function.
$$f ( x ) = - | x - 4 | + 2$$

Accepted Answer

A)  $[ - 4 , \infty )$ 
B)  $[ 2,4 ]$ 
C)  $[ 4 , \infty )$ 
D)  $[ - 2,4 ]$ 
E)  $( - \infty , 2 ]$ 
A)  $[ - 4 , \infty )$ 
B)  $[ 2,4 ]$ 
C)  $[ 4 , \infty )$ 
D)  $[ - 2,4 ]$ 
E)  $( - \infty , 2 ]$

Question 10

Given the following function, $h ( x )$, find two functions $f$ and $g$ such that $( f \circ g ) ( x ) = h ( x )$.
$$h ( x ) = \sqrt [ 3 ] { x ^ { 2 } - 11 }$$

Accepted Answer

A)  $f ( x ) = \sqrt [ 3 ] { x ^ { 2 } } , g ( x ) = - 11$ 
B)  $f ( x ) = \sqrt [ 3 ] { x ^ { 2 } } , g ( x ) = x - 11$ 
C)  $f ( x ) = \sqrt [ 3 ] { x } , g ( x ) = x - 11$ 
D)  $f ( x ) = \sqrt [ 3 ] { x - 11 } , g ( x ) = x ^ { 2 }$ 
E)  $f ( x ) = \sqrt [ 3 ] { x - 11 } , g ( x ) = x + 11$ 
A)  $f ( x ) = \sqrt [ 3 ] { x ^ { 2 } } , g ( x ) = - 11$ 
B)  $f ( x ) = \sqrt [ 3 ] { x ^ { 2 } } , g ( x ) = x - 11$ 
C)  $f ( x ) = \sqrt [ 3 ] { x } , g ( x ) = x - 11$ 
D)  $f ( x ) = \sqrt [ 3 ] { x - 11 } , g ( x ) = x ^ { 2 }$ 
E)  $f ( x ) = \sqrt [ 3 ] { x - 11 } , g ( x ) = x + 11$

Question 11

Determine an equation that may represented by the graph shown below.

Accepted Answer

A)  $f ( x ) = - 1 - \sqrt { 1 - x }$ 
B)  $f ( x ) = - 1 + \sqrt { 1 - x }$ 
C)  $f ( x ) = - 1 - \sqrt { 1 + x }$ 
D)  $f ( x ) = - 1 + \sqrt { 1 + x }$ 
E)  $f ( x ) = 1 - \sqrt { 1 - x }$ 
A)  $f ( x ) = - 1 - \sqrt { 1 - x }$ 
B)  $f ( x ) = - 1 + \sqrt { 1 - x }$ 
C)  $f ( x ) = - 1 - \sqrt { 1 + x }$ 
D)  $f ( x ) = - 1 + \sqrt { 1 + x }$ 
E)  $f ( x ) = 1 - \sqrt { 1 - x }$

Question 12

Compare the graph of the following function with the graph of $f ( x ) = | x |$.
$$y = \left| \frac { 7 } { 9 } x \right|$$

Accepted Answer

A)  vertical shift of $\frac { 7 } { 9 }$ units up 
B)  horizontal stretch of $\frac { 9 } { 7 }$ units 
C)  vertical shrink of $\frac { 7 } { 9 }$ units 
D)  horizontal shrink of $\frac { 7 } { 9 }$ units vertical shift of $\frac { 9 } { 7 }$ units 
E)  horizontal shrink of $\frac { 7 } { 9 }$ units 
A)  vertical shift of $\frac { 7 } { 9 }$ units up 
B)  horizontal stretch of $\frac { 9 } { 7 }$ units 
C)  vertical shrink of $\frac { 7 } { 9 }$ units 
D)  horizontal shrink of $\frac { 7 } { 9 }$ units vertical shift of $\frac { 9 } { 7 }$ units 
E)  horizontal shrink of $\frac { 7 } { 9 }$ units

Question 13

Use the graphs of $f$ and $g$ to evaluate the function.

$$( f \circ g ) ( 1 )$$

Accepted Answer

A)  9 
B)  $- 1$ 
C)  0 
D)  $- 4$ 
E)  $- 2$ 
A)  9 
B)  $- 1$ 
C)  0 
D)  $- 4$ 
E)  $- 2$

Question 14

Determine the domain and range of the inverse function $f ^ { - 1 }$ of the following function $f$ $f ( x ) = - | x + 8 | - 3$, where $x > - 8$

Accepted Answer

A)  Domain: $[ - 8 , \infty )$; Range: $[ - 3 , \infty )$ 
B)  Domain: $( - \infty , - 3 ]$; Range: $[ - 8 , \infty )$ 
C)  Domain: $[ - 8 , - 3 ]$; Range: $[ - 8 , \infty )$ 
D)  Domain: $( - \infty , - 8 ]$; Range: $[ 3 , \infty )$ 
E)  Domain: $( - \infty , \infty )$; Range: $( - \infty , \infty )$ 
A)  Domain: $[ - 8 , \infty )$; Range: $[ - 3 , \infty )$ 
B)  Domain: $( - \infty , - 3 ]$; Range: $[ - 8 , \infty )$ 
C)  Domain: $[ - 8 , - 3 ]$; Range: $[ - 8 , \infty )$ 
D)  Domain: $( - \infty , - 8 ]$; Range: $[ 3 , \infty )$ 
E)  Domain: $( - \infty , \infty )$; Range: $( - \infty , \infty )$

Question 15

Use the graphs of $f$ and $g$, shown below, to graph $h ( x ) = ( f + g ) ( x )$.

Accepted Answer

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

Question 16

Graph the function and determine the interval(s) for which $f ( x ) \geq 0$.
$$f ( x ) = - x ^ { 2 } + 4 x$$

Accepted Answer

A)  $( - \infty , 0 ] \cup [ 4 , \infty )$ 
B)  $[ 0,4 ]$ 
C)  $( 0,4 )$ 
D)  $( - \infty , 0 ) \cup ( 4 , \infty )$ 
E)  $\{ 4 \}$ 
A)  $( - \infty , 0 ] \cup [ 4 , \infty )$ 
B)  $[ 0,4 ]$ 
C)  $( 0,4 )$ 
D)  $( - \infty , 0 ) \cup ( 4 , \infty )$ 
E)  $\{ 4 \}$

Question 17

Which equation does not represent $y$ as a function of $x$ ?

Accepted Answer

A)  $x = 6 y - 9$ 
B)  $x = - 5$ 
C)  $y = x + 5$ 
D)  $y = \left| - 1 - x ^ { 2 } \right|$ 
E)  $y = \sqrt { - 5 + 4 x }$ 
A)  $x = 6 y - 9$ 
B)  $x = - 5$ 
C)  $y = x + 5$ 
D)  $y = \left| - 1 - x ^ { 2 } \right|$ 
E)  $y = \sqrt { - 5 + 4 x }$

Question 18

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

Accepted Answer

A) 
$$f ( x ) = ( x + 1 ) ^ { 2 } - 2$$ 
B) 
$$f ( x ) = ( x - 1 ) ^ { 2 } - 2$$ 
C) 
$$f ( x ) = ( x + 1 ) ^ { 2 } + 2$$ 
D) 
$$f ( x ) = \frac { 1 } { 2 } ( x - 1 ) ^ { 2 } - 2$$ 
E) 
$$f ( x ) = \frac { 1 } { 2 } ( x + 1 ) ^ { 2 } - 2$$ 
A) 
$$f ( x ) = ( x + 1 ) ^ { 2 } - 2$$ 
B) 
$$f ( x ) = ( x - 1 ) ^ { 2 } - 2$$ 
C) 
$$f ( x ) = ( x + 1 ) ^ { 2 } + 2$$ 
D) 
$$f ( x ) = \frac { 1 } { 2 } ( x - 1 ) ^ { 2 } - 2$$ 
E) 
$$f ( x ) = \frac { 1 } { 2 } ( x + 1 ) ^ { 2 } - 2$$

Question 19

Which equation does not represent $y$ as a function of $x$ ?

Accepted Answer

A)  $x = 2 y + 5$ 
B)  $x = 6$ 
C)  $y = - 5 x - 7$ 
D)  $y = \left| 6 + 9 x ^ { 2 } \right|$ 
E)  $y = \sqrt { - 8 + 4 x }$ 
A)  $x = 2 y + 5$ 
B)  $x = 6$ 
C)  $y = - 5 x - 7$ 
D)  $y = \left| 6 + 9 x ^ { 2 } \right|$ 
E)  $y = \sqrt { - 8 + 4 x }$

Question 20

Compare the graph of the following function with the graph of $f ( x ) = | x |$.
$$y = \left| \frac { 4 } { 9 } x \right|$$

Accepted Answer

A)  vertical shift of $\frac { 4 } { 9 }$ units up 
B)  horizontal stretch of $\frac { 9 } { 4 }$ units 
C)  vertical shrink of $\frac { 4 } { 9 }$ units 
D)  horizontal shrink of $\frac { 4 } { 9 }$ units vertical shift of $\frac { 9 } { 4 }$ units 
E)  horizontal shrink of $\frac { 4 } { 9 }$ units 
A)  vertical shift of $\frac { 4 } { 9 }$ units up 
B)  horizontal stretch of $\frac { 9 } { 4 }$ units 
C)  vertical shrink of $\frac { 4 } { 9 }$ units 
D)  horizontal shrink of $\frac { 4 } { 9 }$ units vertical shift of $\frac { 9 } { 4 }$ units 
E)  horizontal shrink of $\frac { 4 } { 9 }$ units

Does the table describe a function? Input value -6 -3 0 3 6 Output value 11 11 11 11 11

Find the slope and y-intercept of the equation of the line. $y = - 2 x + 3$

Use function notation to write $g$ in terms of $f ( x ) = x ^ { 3 }$ . $g ( x ) = - \frac { 1 } { 4 } ( x + 9 ) ^ { 3 }$

Find the domain of the function. $g ( x ) = \sqrt { 25 - x ^ { 2 } }$

Find the domain of the function. $f ( y ) = \sqrt { 9 - y ^ { 2 } }$

Find the domain of the function. $f ( t ) = \sqrt { 64 - t ^ { 2 } }$

Find $g \circ f$ .

Restrict the domain of the following function $f$ so that the function is one-to-one and has an inverse function. $f ( x ) = - | x - 4 | + 2$

Given the following function, $h ( x )$ , find two functions $f$ and $g$ such that $( f \circ g ) ( x ) = h ( x )$ . $h ( x ) = \sqrt [ 3 ] { x ^ { 2 } - 11 }$

Determine an equation that may represented by the graph shown below.

Compare the graph of the following function with the graph of $f ( x ) = | x |$ . $y = \left| \frac { 7 } { 9 } x \right|$

Use the graphs of $f$ and $g$ to evaluate the function. $Use the graphs of f and g to evaluate the function. ( f \circ g ) ( 1 )$ $( f \circ g ) ( 1 )$

Determine the domain and range of the inverse function $f ^ { - 1 }$ of the following function $f$ $f ( x ) = - | x + 8 | - 3$ , where $x > - 8$

Use the graphs of $f$ and $g$ , shown below, to graph $h ( x ) = ( f + g ) ( x )$ .

Graph the function and determine the interval(s) for which $f ( x ) \geq 0$ . $f ( x ) = - x ^ { 2 } + 4 x$ $Graph the function and determine the interval(s) for which f ( x ) \geq 0 . f ( x ) = - x ^ { 2 } + 4 x$

Which equation does not represent $y$ as a function of $x$ ?

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

Which equation does not represent $y$ as a function of $x$ ?

Compare the graph of the following function with the graph of $f ( x ) = | x |$ . $y = \left| \frac { 4 } { 9 } x \right|$

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Linear Systems and Matrices

Sequences, Series, and Probability

Topics in Analytic Geometry

Analytic Geometry in Three Dimensions

Calculus Practice Problems

Filters

Exam 1: Functions and Their Graphs

Does the table describe a function? Input value -6 -3 0 3 6 Output value 11 11 11 11 11

Find the slope and y-intercept of the equation of the line. y=−2x+3y = - 2 x + 3y=−2x+3

Use function notation to write ggg in terms of f(x)=x3f ( x ) = x ^ { 3 }f(x)=x3 . g(x)=−14(x+9)3g ( x ) = - \frac { 1 } { 4 } ( x + 9 ) ^ { 3 }g(x)=−41​(x+9)3

Find the domain of the function. g(x)=25−x2g ( x ) = \sqrt { 25 - x ^ { 2 } }g(x)=25−x2​

Find the domain of the function. f(y)=9−y2f ( y ) = \sqrt { 9 - y ^ { 2 } }f(y)=9−y2​

Find the domain of the function. f(t)=64−t2f ( t ) = \sqrt { 64 - t ^ { 2 } }f(t)=64−t2​

Find g∘fg \circ fg∘f .

Restrict the domain of the following function fff so that the function is one-to-one and has an inverse function. f(x)=−∣x−4∣+2f ( x ) = - | x - 4 | + 2f(x)=−∣x−4∣+2

Given the following function, h(x)h ( x )h(x) , find two functions fff and ggg such that (f∘g)(x)=h(x)( f \circ g ) ( x ) = h ( x )(f∘g)(x)=h(x) . h(x)=x2−113h ( x ) = \sqrt [ 3 ] { x ^ { 2 } - 11 }h(x)=3x2−11​

Determine an equation that may represented by the graph shown below.

Compare the graph of the following function with the graph of f(x)=∣x∣f ( x ) = | x |f(x)=∣x∣ . y=∣79x∣y = \left| \frac { 7 } { 9 } x \right|y=​97​x​

Use the graphs of fff and ggg to evaluate the function. (f∘g)(1)( f \circ g ) ( 1 )(f∘g)(1)

Determine the domain and range of the inverse function f−1f ^ { - 1 }f−1 of the following function fff f(x)=−∣x+8∣−3f ( x ) = - | x + 8 | - 3f(x)=−∣x+8∣−3 , where x>−8x > - 8x>−8

Use the graphs of fff and ggg , shown below, to graph h(x)=(f+g)(x)h ( x ) = ( f + g ) ( x )h(x)=(f+g)(x) .

Graph the function and determine the interval(s) for which f(x)≥0f ( x ) \geq 0f(x)≥0 . f(x)=−x2+4xf ( x ) = - x ^ { 2 } + 4 xf(x)=−x2+4x

Which equation does not represent yyy as a function of xxx ?

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

Which equation does not represent yyy as a function of xxx ?

Compare the graph of the following function with the graph of f(x)=∣x∣f ( x ) = | x |f(x)=∣x∣ . y=∣49x∣y = \left| \frac { 4 } { 9 } x \right|y=​94​x​

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Linear Systems and Matrices

Sequences, Series, and Probability

Topics in Analytic Geometry

Analytic Geometry in Three Dimensions

Calculus Practice Problems

Filters

Find the slope and y-intercept of the equation of the line. $y = - 2 x + 3$

Use function notation to write $g$ in terms of $f ( x ) = x ^ { 3 }$ . $g ( x ) = - \frac { 1 } { 4 } ( x + 9 ) ^ { 3 }$

Find the domain of the function. $g ( x ) = \sqrt { 25 - x ^ { 2 } }$

Find the domain of the function. $f ( y ) = \sqrt { 9 - y ^ { 2 } }$

Find the domain of the function. $f ( t ) = \sqrt { 64 - t ^ { 2 } }$

Find $g \circ f$ .

Restrict the domain of the following function $f$ so that the function is one-to-one and has an inverse function. $f ( x ) = - | x - 4 | + 2$

Given the following function, $h ( x )$ , find two functions $f$ and $g$ such that $( f \circ g ) ( x ) = h ( x )$ . $h ( x ) = \sqrt [ 3 ] { x ^ { 2 } - 11 }$

Compare the graph of the following function with the graph of $f ( x ) = | x |$ . $y = \left| \frac { 7 } { 9 } x \right|$

Use the graphs of $f$ and $g$ to evaluate the function. $Use the graphs of f and g to evaluate the function. ( f \circ g ) ( 1 )$ $( f \circ g ) ( 1 )$

Determine the domain and range of the inverse function $f ^ { - 1 }$ of the following function $f$ $f ( x ) = - | x + 8 | - 3$ , where $x > - 8$

Use the graphs of $f$ and $g$ , shown below, to graph $h ( x ) = ( f + g ) ( x )$ .

Graph the function and determine the interval(s) for which $f ( x ) \geq 0$ . $f ( x ) = - x ^ { 2 } + 4 x$ $Graph the function and determine the interval(s) for which f ( x ) \geq 0 . f ( x ) = - x ^ { 2 } + 4 x$

Which equation does not represent $y$ as a function of $x$ ?

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

Which equation does not represent $y$ as a function of $x$ ?

Compare the graph of the following function with the graph of $f ( x ) = | x |$ . $y = \left| \frac { 4 } { 9 } x \right|$