Question 1

Find all real values of $x$ such that $f ( x ) = 0$.
$f ( x ) = \frac { 7 x - 5 } { 7 }$

Accepted Answer

A)  $\frac { 5 } { 49 }$ 
B)  $\pm \frac { 5 } { 49 }$ 
C)  $\pm \frac { 5 } { 7 }$ 
D)  $\frac { 5 } { 7 }$ 
E)  $- \frac { 5 } { 7 }$ 
A)  $\frac { 5 } { 49 }$ 
B)  $\pm \frac { 5 } { 49 }$ 
C)  $\pm \frac { 5 } { 7 }$ 
D)  $\frac { 5 } { 7 }$ 
E)  $- \frac { 5 } { 7 }$

Question 2

Use the functions $f ( x ) = \frac { 1 } { 125 } x - 5$ and $g ( x ) = x ^ { 3 }$ to find $( f \circ g ) ^ { - 1 }$.

Accepted Answer

A)  $( f \circ g ) ^ { - 1 } = \frac { x ^ { 3 } + 5 } { 5 }$ 
B)  $( f \circ g ) ^ { - 1 } = \frac { x ^ { 3 } - 625 } { 125 }$ 
C)  $( f \circ g ) ^ { - 1 } = \frac { \sqrt [ 3 ] { x + 5 } } { 5 }$ 
D)  $( f \circ g ) ^ { - 1 } = 5 x + 5$ 
E)  $( f \circ g ) ^ { - 1 } = 5 \sqrt [ 3 ] { x + 5 }$ 
A)  $( f \circ g ) ^ { - 1 } = \frac { x ^ { 3 } + 5 } { 5 }$ 
B)  $( f \circ g ) ^ { - 1 } = \frac { x ^ { 3 } - 625 } { 125 }$ 
C)  $( f \circ g ) ^ { - 1 } = \frac { \sqrt [ 3 ] { x + 5 } } { 5 }$ 
D)  $( f \circ g ) ^ { - 1 } = 5 x + 5$ 
E)  $( f \circ g ) ^ { - 1 } = 5 \sqrt [ 3 ] { x + 5 }$

Question 3

Show algebraically that the functions $f$ and $g$ shown below are inverse functions.
$f ( x ) = \sqrt [ 3 ] { 8 x - 7 } , \ g ( x ) = \frac { x ^ { 3 } + 7 } { 8 }$

Accepted Answer

A) 
$\begin{aligned}
f(g(x)) &=\sqrt[3]{8\left(\frac{x^{3}+7}{8}\right)-7} \
&=\sqrt[3]{\left(x^{3}+56\right)-56} \
&=\sqrt[3]{x^{3}+56-56} \
&=\sqrt[3]{x^{3}} \
&=x
\end{aligned}$

$\begin{aligned}
g(f(x)) &=\frac{(\sqrt[3]{8 x-7})^{3}+7}{8} \
&=\frac{8 x-7^{3}+7^{3}}{8} \
&=\quad \frac{8 x}{8}\
&=x
\end{aligned}$ 
B) $\begin{aligned}
f(g(x)) &=\sqrt[3]{8\left(\frac{x^{3}+7}{8}\right)-7} \
&=\sqrt[3]{\left(x^{3}+7\right)-7} \
&=\sqrt[3]{x^{3}+7-7} \
&=\sqrt[3]{x^{3}} \
&=x
\end{aligned}$

$\begin{aligned}
g(f(x)) &=& \frac{(\sqrt[3]{8 x-7})^{3}+7}{8} \
&=& \frac{8 x-7+7}{8} \
&=& \frac{8 x}{8} \
&=& x
\end{aligned}$ 
C) $\begin{aligned}
f(g(x)) &=\sqrt[3]{8\left(\frac{x^{3}+7}{8}\right)-7} \
&=\sqrt[3]{\left(\frac{8 x^{3}+7}{8}\right)-7} \
&=\sqrt[3]{x^{3}+7-7} \
&=\sqrt[3]{x^{3}} \
&=x
\end{aligned}$

$\begin{aligned}
g(f(x)) &=\frac{(\sqrt[3]{8 x-7})^{3}+7}{8} \
&=\frac{8^{3} x-7+7}{8^{3}} \
&=\frac{8^{3} x}{8^{3}} \
&=x
\end{aligned}$ 
D) $\begin{aligned}
f(g(x)) &=\sqrt[3]{8\left(\frac{x^{3}+7}{8}\right)-7} \
&=\sqrt[3]{\left(8 x^{3}+56\right)-56} \
&=\sqrt[3]{8 x^{3}+56-56} \
&=\sqrt[3]{8 x^{3}} \
&=x
\end{aligned}$

$\begin{aligned}
g(f(x)) &=\frac{(\sqrt[3]{8 x-7})^{3}+7}{8} \
&=\frac{8^{3} x-7^{3}+7^{3}}{8^{3}} \
&=\frac{8^{3} x}{8^{3}} \
&=\quad x
\end{aligned}$ 
E) $\begin{aligned}
f(g(x)) &=\sqrt[3]{8\left(\frac{x^{3}+7}{8}\right)-7} \
&=\sqrt[3]{\left(x^{3}+\frac{7}{8}\right)-7} \
&=\sqrt[3]{x^{3}+\frac{0}{8}} \
&=\sqrt[3]{x^{3}} \
&=x
\end{aligned}$

$\begin{aligned}
g(f(x)) &=\frac{(\sqrt[3]{8 x-7})^{3}+7}{8} \
&=\frac{24 x-21+21}{24} \
&=\quad \frac{24 x}{24} \
&=\quad x
\end{aligned}$ 
A) 
$\begin{aligned}
f(g(x)) &=\sqrt[3]{8\left(\frac{x^{3}+7}{8}\right)-7} \
&=\sqrt[3]{\left(x^{3}+56\right)-56} \
&=\sqrt[3]{x^{3}+56-56} \
&=\sqrt[3]{x^{3}} \
&=x
\end{aligned}$

$\begin{aligned}
g(f(x)) &=\frac{(\sqrt[3]{8 x-7})^{3}+7}{8} \
&=\frac{8 x-7^{3}+7^{3}}{8} \
&=\quad \frac{8 x}{8}\
&=x
\end{aligned}$ 
B) $\begin{aligned}
f(g(x)) &=\sqrt[3]{8\left(\frac{x^{3}+7}{8}\right)-7} \
&=\sqrt[3]{\left(x^{3}+7\right)-7} \
&=\sqrt[3]{x^{3}+7-7} \
&=\sqrt[3]{x^{3}} \
&=x
\end{aligned}$

$\begin{aligned}
g(f(x)) &=& \frac{(\sqrt[3]{8 x-7})^{3}+7}{8} \
&=& \frac{8 x-7+7}{8} \
&=& \frac{8 x}{8} \
&=& x
\end{aligned}$ 
C) $\begin{aligned}
f(g(x)) &=\sqrt[3]{8\left(\frac{x^{3}+7}{8}\right)-7} \
&=\sqrt[3]{\left(\frac{8 x^{3}+7}{8}\right)-7} \
&=\sqrt[3]{x^{3}+7-7} \
&=\sqrt[3]{x^{3}} \
&=x
\end{aligned}$

$\begin{aligned}
g(f(x)) &=\frac{(\sqrt[3]{8 x-7})^{3}+7}{8} \
&=\frac{8^{3} x-7+7}{8^{3}} \
&=\frac{8^{3} x}{8^{3}} \
&=x
\end{aligned}$ 
D) $\begin{aligned}
f(g(x)) &=\sqrt[3]{8\left(\frac{x^{3}+7}{8}\right)-7} \
&=\sqrt[3]{\left(8 x^{3}+56\right)-56} \
&=\sqrt[3]{8 x^{3}+56-56} \
&=\sqrt[3]{8 x^{3}} \
&=x
\end{aligned}$

$\begin{aligned}
g(f(x)) &=\frac{(\sqrt[3]{8 x-7})^{3}+7}{8} \
&=\frac{8^{3} x-7^{3}+7^{3}}{8^{3}} \
&=\frac{8^{3} x}{8^{3}} \
&=\quad x
\end{aligned}$ 
E) $\begin{aligned}
f(g(x)) &=\sqrt[3]{8\left(\frac{x^{3}+7}{8}\right)-7} \
&=\sqrt[3]{\left(x^{3}+\frac{7}{8}\right)-7} \
&=\sqrt[3]{x^{3}+\frac{0}{8}} \
&=\sqrt[3]{x^{3}} \
&=x
\end{aligned}$

$\begin{aligned}
g(f(x)) &=\frac{(\sqrt[3]{8 x-7})^{3}+7}{8} \
&=\frac{24 x-21+21}{24} \
&=\quad \frac{24 x}{24} \
&=\quad x
\end{aligned}$

Question 4

Does the table describe a function?
$\begin{array}{|c|c|c|c|c|c|}
\hline \text { Input value } & 5 & 10 & 13 & 10 & 5 \
\hline \text { Output value } & -13 & -9 & 0 & 9 & 13 \
\hline
\end{array}$

Accepted Answer

A) True 
 B)False

Question 5

Evaluate the function at the specified value of the independent variable and simplify.
$f ( y ) = 2 y + 7$
$f ( - 1.4 )$

Accepted Answer

A)  $- 2.8 y + 14$ 
B)  $- 9.8$ 
C)  $4.2$ 
D)  $- 1.4 y + 7$ 
E)  $- 1.4 y - 7$ 
A)  $- 2.8 y + 14$ 
B)  $- 9.8$ 
C)  $4.2$ 
D)  $- 1.4 y + 7$ 
E)  $- 1.4 y - 7$

Question 6

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

Accepted Answer

A)  $f ( x ) = ( x - 1 ) ^ { 3 } + 2$ 
B)  $f ( x ) = - ( x - 1 ) ^ { 3 } + 2$ 
C)  $f ( x ) = - ( x - 1 ) ^ { 3 } - 2$ 
D)  $f ( x ) = - ( x + 1 ) ^ { 3 } - 2$ 
E)  $f ( x ) = - ( x + 1 ) ^ { 3 } + 2$ 
A)  $f ( x ) = ( x - 1 ) ^ { 3 } + 2$ 
B)  $f ( x ) = - ( x - 1 ) ^ { 3 } + 2$ 
C)  $f ( x ) = - ( x - 1 ) ^ { 3 } - 2$ 
D)  $f ( x ) = - ( x + 1 ) ^ { 3 } - 2$ 
E)  $f ( x ) = - ( x + 1 ) ^ { 3 } + 2$

Question 7

Given $f ( x ) = \frac { 10 } { x ^ { 2 } - 9 }$ and $g ( x ) = x + 3$ determine the domain of $f \circ g$.

Accepted Answer

A)  $( - \infty , - 3 ) \cup ( 3 , \infty )$ 
B)  $( - \infty , - 6 ) \cup ( - 6,0 ) \cup ( 0 , \infty )$ 
C)  $\left( - \infty , - \frac { 10 } { 3 } \right) \cup \left( \frac { 10 } { 3 } , \infty \right)$ 
D)  $( - \infty , - 3 ) \cup ( - 3,3 ) \cup ( 3 , \infty )$ 
E)  $( - \infty , \infty )$ 
A)  $( - \infty , - 3 ) \cup ( 3 , \infty )$ 
B)  $( - \infty , - 6 ) \cup ( - 6,0 ) \cup ( 0 , \infty )$ 
C)  $\left( - \infty , - \frac { 10 } { 3 } \right) \cup \left( \frac { 10 } { 3 } , \infty \right)$ 
D)  $( - \infty , - 3 ) \cup ( - 3,3 ) \cup ( 3 , \infty )$ 
E)  $( - \infty , \infty )$

Question 8

Evaluate the function at the specified value of the independent variable and simplify. 
$q ( p ) = \frac { - 2 p } { 5 p - 2 }$
$q ( x - 9 )$

Accepted Answer

A)  $\frac { - 2 x + 18 } { 5 x - 47 }$ 
B)  $\frac { - 2 x - 18 } { 5 x - 47 }$ 
C)  $\frac { - 2 p + 18 } { 5 p - 47 }$ 
D)  $\frac { 18 } { 43 }$ 
E)  $- \frac { 18 } { 47 }$ 
A)  $\frac { - 2 x + 18 } { 5 x - 47 }$ 
B)  $\frac { - 2 x - 18 } { 5 x - 47 }$ 
C)  $\frac { - 2 p + 18 } { 5 p - 47 }$ 
D)  $\frac { 18 } { 43 }$ 
E)  $- \frac { 18 } { 47 }$

Question 9

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

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 10

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, Fk= 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. $$\begin{array} { | c | c | } 
\hline \text { Force, } \boldsymbol { F } & \text { Elongation, } \boldsymbol { d } \
\hline 20 & 1.4 \
\hline 40 & 2.5 \
\hline 60 & 4.0 \
\hline 80 & 5.3 \
\hline 100 & 6.6 \
\hline
\end{array}$$ Find the equation of the line that seems to best fit the data. Use the model to estimate
The elongation of the spring when a force of 55 kilograms is applied. Round your
Answer to one decimal place.

Accepted Answer

A)  7.2 centimeters 
B)  5.4 centimeters 
C)  1.8 centimeters 
D)  3.6 centimeters 
E)  2.7 centimeters 
A)  7.2 centimeters 
B)  5.4 centimeters 
C)  1.8 centimeters 
D)  3.6 centimeters 
E)  2.7 centimeters

Question 11

Determine whether the function has an inverse function. If it does, find the inverse function.
$$f ( x ) = x ^ { 2 } + 5$$

Accepted Answer

A)  No inverse function exists. 
B)  $f ^ { - 1 } ( x ) = \sqrt { x } + 5 , x \geq 0$ 
C)  $f ^ { - 1 } ( x ) = \sqrt { x } - 5$ 
D)  $f ^ { - 1 } ( x ) = \sqrt { x + 5 } , x \geq - 6$ 
E)  $f ^ { - 1 } ( x ) = \sqrt { x - 5 }$ 
A)  No inverse function exists. 
B)  $f ^ { - 1 } ( x ) = \sqrt { x } + 5 , x \geq 0$ 
C)  $f ^ { - 1 } ( x ) = \sqrt { x } - 5$ 
D)  $f ^ { - 1 } ( x ) = \sqrt { x + 5 } , x \geq - 6$ 
E)  $f ^ { - 1 } ( x ) = \sqrt { x - 5 }$

Question 12

Estimate the slope of the line.

Accepted Answer

A)  $- 5$ 
B)  0 
C)  5 
D)  $\frac { 1 } { 5 }$ 
E)  $\frac { 2 } { 5 }$ 
A)  $- 5$ 
B)  0 
C)  5 
D)  $\frac { 1 } { 5 }$ 
E)  $\frac { 2 } { 5 }$

Question 13

Find the inverse function of f. 
$f ( x ) = x ^ { 9 } - 2$

Accepted Answer

A)  $f ^ { - 1 } ( x ) = - \sqrt [ 9 ] { x } - 2$ 
B)  $f ^ { - 1 } ( x ) = \sqrt [ 9 ] { x } - 2$ 
C)  $f ^ { - 1 } ( x ) = - \sqrt [ 9 ] { x - 2 }$ 
D)  $f ^ { - 1 } ( x ) = \sqrt [ 9 ] { x + 2 }$ 
E)  $f ^ { - 1 } ( x ) = \sqrt [ 9 ] { x } + 2$ 
A)  $f ^ { - 1 } ( x ) = - \sqrt [ 9 ] { x } - 2$ 
B)  $f ^ { - 1 } ( x ) = \sqrt [ 9 ] { x } - 2$ 
C)  $f ^ { - 1 } ( x ) = - \sqrt [ 9 ] { x - 2 }$ 
D)  $f ^ { - 1 } ( x ) = \sqrt [ 9 ] { x + 2 }$ 
E)  $f ^ { - 1 } ( x ) = \sqrt [ 9 ] { x } + 2$

Question 14

Find $g \circ f$.
$\begin{array} { l l } f ( x ) = x + 2 & g ( x ) = x ^ { 2 } \  \end{array}$

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)  $( g \circ f ) ( x ) = x ^ { 2 } + 4 x + 4$ 
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)  $( g \circ f ) ( x ) = x ^ { 2 } + 4 x + 4$

Question 15

Determine whether the function is even, odd, or neither.
$$f ( x ) = 4 x ^ { 3 } - 2 x$$

Accepted Answer

A)  neither 
B)  even 
C)  odd 
A)  neither 
B)  even 
C)  odd

Question 16

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

Accepted Answer

A)  $x = - 9 y + 2$ 
B)  $x = - 1$ 
C)  $y = 7 x - 9$ 
D)  $y = \left| 6 - x ^ { 2 } \right|$ 
E)  $y = \sqrt { - 9 + 6 x }$ 
A)  $x = - 9 y + 2$ 
B)  $x = - 1$ 
C)  $y = 7 x - 9$ 
D)  $y = \left| 6 - x ^ { 2 } \right|$ 
E)  $y = \sqrt { - 9 + 6 x }$

Question 17

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 18

Find $f \circ g$.
$f ( x ) = x + 2 \quad g ( x ) = \frac { 5 } { x ^ { 2 } - 4 }$

Accepted Answer

A)  $( f \circ g ) ( x ) = \frac { 5 } { x ^ { 2 } }$ 
B)  $( f \circ g ) ( x ) = \frac { 5 } { x ^ { 2 } + 4 x }$ 
C)  $( f \circ g ) ( x ) = \frac { 2 x ^ { 2 } + 3 } { x ^ { 2 } - 4 }$ 
D)  $( f \circ g ) ( x ) = \frac { 7 } { x ^ { 2 } - 4 }$ 
E)  $( f \circ g ) ( x ) = \frac { 2 x ^ { 2 } - 3 } { x ^ { 2 } - 4 }$ 
A)  $( f \circ g ) ( x ) = \frac { 5 } { x ^ { 2 } }$ 
B)  $( f \circ g ) ( x ) = \frac { 5 } { x ^ { 2 } + 4 x }$ 
C)  $( f \circ g ) ( x ) = \frac { 2 x ^ { 2 } + 3 } { x ^ { 2 } - 4 }$ 
D)  $( f \circ g ) ( x ) = \frac { 7 } { x ^ { 2 } - 4 }$ 
E)  $( f \circ g ) ( x ) = \frac { 2 x ^ { 2 } - 3 } { x ^ { 2 } - 4 }$

Question 19

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 horizontal shrink of $\frac { 4 } { 9 }$ units 
D)  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 horizontal shrink of $\frac { 4 } { 9 }$ units 
D)  vertical shift of $\frac { 9 } { 4 }$ units 
E)  horizontal shrink of $\frac { 4 } { 9 }$ units

Question 20

Use a graphing utility to graph the function and visually determine the intervals over which the function is increasing, decreasing, or constant.
$f ( x ) = 2 x ^ { 4 } - 4 x ^ { 2 }$

Accepted Answer

A)  decreasing on $( 0,0 )$
increasing on $( 0 , \infty )$
increasing on $( - \infty , - 1 )$ 
B)  decreasing on $( - 1,0 )$
increasing on $( 0,1 )$
decreasing on $( 1 , \infty )$
decreasing on $( - \infty , - 1 )$ 
C)  increasing on $( - 1,1 )$
decreasing on $( 1 , \infty )$
increasing on $( - \infty , 0 )$ 
D) 
decreasing on $( 0 , \infty )$
decreasing on $( - \infty , - 1 )$
increasing on $( - 1,0 )$ 
E) 
decreasing on $( 0,1 )$
increasing on $( 1 , \infty )$ 
A)  decreasing on $( 0,0 )$
increasing on $( 0 , \infty )$
increasing on $( - \infty , - 1 )$ 
B)  decreasing on $( - 1,0 )$
increasing on $( 0,1 )$
decreasing on $( 1 , \infty )$
decreasing on $( - \infty , - 1 )$ 
C)  increasing on $( - 1,1 )$
decreasing on $( 1 , \infty )$
increasing on $( - \infty , 0 )$ 
D) 
decreasing on $( 0 , \infty )$
decreasing on $( - \infty , - 1 )$
increasing on $( - 1,0 )$ 
E) 
decreasing on $( 0,1 )$
increasing on $( 1 , \infty )$

Find all real values of $x$ such that $f ( x ) = 0$ . $f ( x ) = \frac { 7 x - 5 } { 7 }$

Use the functions $f ( x ) = \frac { 1 } { 125 } x - 5$ and $g ( x ) = x ^ { 3 }$ to find $( f \circ g ) ^ { - 1 }$ .

Show algebraically that the functions $f$ and $g$ shown below are inverse functions. $f ( x ) = \sqrt [ 3 ] { 8 x - 7 } , \ g ( x ) = \frac { x ^ { 3 } + 7 } { 8 }$

Does the table describe a function? Input value 5 10 13 10 5 Output value -13 -9 0 9 13

Evaluate the function at the specified value of the independent variable and simplify. $f ( y ) = 2 y + 7$ $f ( - 1.4 )$

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

Given $f ( x ) = \frac { 10 } { x ^ { 2 } - 9 }$ and $g ( x ) = x + 3$ determine the domain of $f \circ g$ .

Evaluate the function at the specified value of the independent variable and simplify. $q ( p ) = \frac { - 2 p } { 5 p - 2 }$ $q ( x - 9 )$

Given the following function, h( x), find two functions f and g such that (f\circg)(x)=h(x). h(x)=

Determine whether the function has an inverse function. If it does, find the inverse function. $f ( x ) = x ^ { 2 } + 5$

Estimate the slope of the line.

Find the inverse function of f. $f ( x ) = x ^ { 9 } - 2$

Find $g \circ f$ . f(x)=x+2 g(x)=

Determine whether the function is even, odd, or neither. $f ( x ) = 4 x ^ { 3 } - 2 x$

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

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

Find $f \circ g$ . $f ( x ) = x + 2 \quad g ( x ) = \frac { 5 } { x ^ { 2 } - 4 }$

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

Use a graphing utility to graph the function and visually determine the intervals over which the function is increasing, decreasing, or constant. $f ( x ) = 2 x ^ { 4 } - 4 x ^ { 2 }$

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

Limits and an Introduction to Calculus

Review of Graphs, Equations, and Inequalities

Filters

Exam 1: Functions and Their Graphs

Find all real values of xxx such that f(x)=0f ( x ) = 0f(x)=0 . f(x)=7x−57f ( x ) = \frac { 7 x - 5 } { 7 }f(x)=77x−5​

Use the functions f(x)=1125x−5f ( x ) = \frac { 1 } { 125 } x - 5f(x)=1251​x−5 and g(x)=x3g ( x ) = x ^ { 3 }g(x)=x3 to find (f∘g)−1( f \circ g ) ^ { - 1 }(f∘g)−1 .

Show algebraically that the functions fff and ggg shown below are inverse functions. f(x)=8x−73, g(x)=x3+78f ( x ) = \sqrt [ 3 ] { 8 x - 7 } , \ g ( x ) = \frac { x ^ { 3 } + 7 } { 8 }f(x)=38x−7​, g(x)=8x3+7​

Does the table describe a function? Input value 5 10 13 10 5 Output value -13 -9 0 9 13

Evaluate the function at the specified value of the independent variable and simplify. f(y)=2y+7f ( y ) = 2 y + 7f(y)=2y+7 f(−1.4)f ( - 1.4 )f(−1.4)

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

Given f(x)=10x2−9f ( x ) = \frac { 10 } { x ^ { 2 } - 9 }f(x)=x2−910​ and g(x)=x+3g ( x ) = x + 3g(x)=x+3 determine the domain of f∘gf \circ gf∘g .

Evaluate the function at the specified value of the independent variable and simplify. q(p)=−2p5p−2q ( p ) = \frac { - 2 p } { 5 p - 2 }q(p)=5p−2−2p​ q(x−9)q ( x - 9 )q(x−9)

Given the following function, h( x), find two functions f and g such that (f\circg)(x)=h(x). h(x)=

Determine whether the function has an inverse function. If it does, find the inverse function. f(x)=x2+5f ( x ) = x ^ { 2 } + 5f(x)=x2+5

Estimate the slope of the line.

Find the inverse function of f. f(x)=x9−2f ( x ) = x ^ { 9 } - 2f(x)=x9−2

Find g∘fg \circ fg∘f . f(x)=x+2 g(x)=

Determine whether the function is even, odd, or neither. f(x)=4x3−2xf ( x ) = 4 x ^ { 3 } - 2 xf(x)=4x3−2x

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

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

Find f∘gf \circ gf∘g . f(x)=x+2g(x)=5x2−4f ( x ) = x + 2 \quad g ( x ) = \frac { 5 } { x ^ { 2 } - 4 }f(x)=x+2g(x)=x2−45​

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​

Use a graphing utility to graph the function and visually determine the intervals over which the function is increasing, decreasing, or constant. f(x)=2x4−4x2f ( x ) = 2 x ^ { 4 } - 4 x ^ { 2 }f(x)=2x4−4x2

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

Limits and an Introduction to Calculus

Review of Graphs, Equations, and Inequalities

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Find all real values of $x$ such that $f ( x ) = 0$ . $f ( x ) = \frac { 7 x - 5 } { 7 }$

Use the functions $f ( x ) = \frac { 1 } { 125 } x - 5$ and $g ( x ) = x ^ { 3 }$ to find $( f \circ g ) ^ { - 1 }$ .

Show algebraically that the functions $f$ and $g$ shown below are inverse functions. $f ( x ) = \sqrt [ 3 ] { 8 x - 7 } , \ g ( x ) = \frac { x ^ { 3 } + 7 } { 8 }$

Evaluate the function at the specified value of the independent variable and simplify. $f ( y ) = 2 y + 7$ $f ( - 1.4 )$

Given $f ( x ) = \frac { 10 } { x ^ { 2 } - 9 }$ and $g ( x ) = x + 3$ determine the domain of $f \circ g$ .

Evaluate the function at the specified value of the independent variable and simplify. $q ( p ) = \frac { - 2 p } { 5 p - 2 }$ $q ( x - 9 )$

Determine whether the function has an inverse function. If it does, find the inverse function. $f ( x ) = x ^ { 2 } + 5$

Find the inverse function of f. $f ( x ) = x ^ { 9 } - 2$

Find $g \circ f$ . f(x)=x+2 g(x)=

Determine whether the function is even, odd, or neither. $f ( x ) = 4 x ^ { 3 } - 2 x$

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

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

Find $f \circ g$ . $f ( x ) = x + 2 \quad g ( x ) = \frac { 5 } { x ^ { 2 } - 4 }$

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

Use a graphing utility to graph the function and visually determine the intervals over which the function is increasing, decreasing, or constant. $f ( x ) = 2 x ^ { 4 } - 4 x ^ { 2 }$