Question 1

Write the slope-intercept form of the equation of the line through the given point parallel to the given line.
point: $( 3 , - 4 ) \quad$ line: $28 x + 7 y = - 4$

Accepted Answer

A)  $y = - \frac { 1 } { 28 } x - \frac { 109 } { 28 }$ 
B)  $y = \frac { 1 } { 4 } x - \frac { 19 } { 4 }$ 
C)  $y = 28 x + 80$ 
D)  $y = - 4 x + 8$ 
E)  $y = - 4 x - 13$ 
A)  $y = - \frac { 1 } { 28 } x - \frac { 109 } { 28 }$ 
B)  $y = \frac { 1 } { 4 } x - \frac { 19 } { 4 }$ 
C)  $y = 28 x + 80$ 
D)  $y = - 4 x + 8$ 
E)  $y = - 4 x - 13$

Question 2

Use the graphs of $y = f ( x )$ and $y = g ( x )$ to evaluate $\left( g ^ { - 1 } \circ f ^ { - 1 } \right) ( - 4 )$

Accepted Answer

A)  4 
B)  $1.3$ 
C)  0 
D)  $- 2$ 
E)  $- 2.5$ 
A)  4 
B)  $1.3$ 
C)  0 
D)  $- 2$ 
E)  $- 2.5$

Question 3

Compare the graph of the following function with the graph of $f ( x ) = | x |$.
$$y = \left| \frac { 3 } { 4 } x \right|$$

Accepted Answer

A)  vertical shift of $\frac { 3 } { 4 }$ units up 
B)  horizontal stretch of $\frac { 4 } { 3 }$ units 
C)  vertical shrink of $\frac { 3 } { 4 }$ units horizontal shrink of $\frac { 3 } { 4 }$ units 
D)  vertical shift of $\frac { 4 } { 3 }$ units 
E)  horizontal shrink of $\frac { 3 } { 4 }$ units 
A)  vertical shift of $\frac { 3 } { 4 }$ units up 
B)  horizontal stretch of $\frac { 4 } { 3 }$ units 
C)  vertical shrink of $\frac { 3 } { 4 }$ units horizontal shrink of $\frac { 3 } { 4 }$ units 
D)  vertical shift of $\frac { 4 } { 3 }$ units 
E)  horizontal shrink of $\frac { 3 } { 4 }$ units

Question 4

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 5

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 6

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. $\begin{array} { | c | c | } 
\hline \text { Force, } \boldsymbol { F } & \text { Elongation, } \boldsymbol { d } \
\hline 20 & 3.5 \
\hline 40 & 6.3 \
\hline 60 & 10.0 \
\hline 80 & 13.3 \
\hline 100 & 16.5 \
\hline
\end{array}$
 Find the equation of the line that seems to best fit the data.

Accepted Answer

A)  F =12.098d 
B)  Fd= 3.024 
C)  F = 6.049d 
D)  Fd= 4.537 
E)  F = 7.561d 
A)  F =12.098d 
B)  Fd= 3.024 
C)  F = 6.049d 
D)  Fd= 4.537 
E)  F = 7.561d

Question 7

Use function notation to write $g$ in terms of $f ( x ) = \sqrt { x }$.
$g ( x ) = - \frac { 1 } { 3 } \sqrt { x - 8 } + 7$

Accepted Answer

A)  $g ( x ) = - f ( x - 8 ) + 6$ 
B)  $\quad g ( x ) = - \frac { 1 } { 3 } f ( x ) - 1$ 
C)  $\quad g ( x ) = - \frac { 1 } { 3 } f ( x - 8 ) + 7$ 
D)  $g ( x ) = f ( x ) + 7$ 
E)  $\quad g ( x ) = f ( x - 8 ) - \frac { 7 } { 3 }$ 
A)  $g ( x ) = - f ( x - 8 ) + 6$ 
B)  $\quad g ( x ) = - \frac { 1 } { 3 } f ( x ) - 1$ 
C)  $\quad g ( x ) = - \frac { 1 } { 3 } f ( x - 8 ) + 7$ 
D)  $g ( x ) = f ( x ) + 7$ 
E)  $\quad g ( x ) = f ( x - 8 ) - \frac { 7 } { 3 }$

Question 8

Determine the domain of $g ( x ) = \frac { 1 } { x ^ { 2 } - 81 }$.

Accepted Answer

A)  $[ - 9,9 ]$ 
B)  $( - 9,0 ] \cup [ 0,9 )$ 
C)  $( - \infty , - 9 ) \cup ( - 9,9 ) \cup ( 9 , \infty )$ 
D)  $( - \infty , - 9 ] \cup [ 9 , \infty )$ 
E)  $( - \infty , \infty )$ 
A)  $[ - 9,9 ]$ 
B)  $( - 9,0 ] \cup [ 0,9 )$ 
C)  $( - \infty , - 9 ) \cup ( - 9,9 ) \cup ( 9 , \infty )$ 
D)  $( - \infty , - 9 ] \cup [ 9 , \infty )$ 
E)  $( - \infty , \infty )$

Question 9

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 10

Determine whether lines $L _ { 1 }$ and $L _ { 2 }$ passing through the pairs of points are parallel, perpendicular, or neither.
$L _ { 1 } : ( 7 , - 4 ) , ( - 9 , - 1 )$ $L _ { 2 } : ( 4 , - 6 ) , ( - 3,9 )$

Accepted Answer

A)  parallel 
B)  perpendicular 
C)  neither 
A)  parallel 
B)  perpendicular 
C)  neither

Question 11

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 12

Find the inverse function of $f$.
$f ( x ) = x ^ { 5 } + 5$

Accepted Answer

A)  $f ^ { - 1 } ( x ) = - \sqrt [ 5 ] { x } + 5$ 
B)  $f ^ { - 1 } ( x ) = \sqrt [ 5 ] { x } + 5$ 
C)  $f ^ { - 1 } ( x ) = - \sqrt [ 5 ] { x + 5 }$ 
D)  $f ^ { - 1 } ( x ) = \sqrt [ 5 ] { x - 5 }$ 
E)  $f ^ { - 1 } ( x ) = \sqrt [ 5 ] { x } - 5$ 
A)  $f ^ { - 1 } ( x ) = - \sqrt [ 5 ] { x } + 5$ 
B)  $f ^ { - 1 } ( x ) = \sqrt [ 5 ] { x } + 5$ 
C)  $f ^ { - 1 } ( x ) = - \sqrt [ 5 ] { x + 5 }$ 
D)  $f ^ { - 1 } ( x ) = \sqrt [ 5 ] { x - 5 }$ 
E)  $f ^ { - 1 } ( x ) = \sqrt [ 5 ] { x } - 5$

Question 13

Find $( f g ) ( x )$
$f ( x ) = \sqrt { - 5 x } \quad g ( x ) = \sqrt { - 8 x + 6 }$

Accepted Answer

A)  $( f g ) ( x ) = 2 x \sqrt { 10 } - \sqrt { 30 x }$ 
B)  $( f g ) ( x ) = 2 x \sqrt { 10 - 30 x }$ 
C)  $( f g ) ( x ) = \sqrt { - 13 x + 6 }$ 
D)  $( f g ) ( x ) = \sqrt { 40 x ^ { 2 } + 6 }$ 
E)  $( f g ) ( x ) = \sqrt { 40 x ^ { 2 } - 30 x }$ 
A)  $( f g ) ( x ) = 2 x \sqrt { 10 } - \sqrt { 30 x }$ 
B)  $( f g ) ( x ) = 2 x \sqrt { 10 - 30 x }$ 
C)  $( f g ) ( x ) = \sqrt { - 13 x + 6 }$ 
D)  $( f g ) ( x ) = \sqrt { 40 x ^ { 2 } + 6 }$ 
E)  $( f g ) ( x ) = \sqrt { 40 x ^ { 2 } - 30 x }$

Question 14

Find the inverse function of $f ( x ) = 8 x + 3$

Accepted Answer

A)  $g ( x ) = \frac { x - 3 } { 8 }$ 
B)  $g ( x ) = 3 x + 8$ 
C)  $g ( x ) = \frac { x + 3 } { 8 }$ 
D)  $g ( x ) = \frac { x } { 3 }$ 
E)  $g ( x ) = \frac { 1 } { 8 } x - 3$ 
A)  $g ( x ) = \frac { x - 3 } { 8 }$ 
B)  $g ( x ) = 3 x + 8$ 
C)  $g ( x ) = \frac { x + 3 } { 8 }$ 
D)  $g ( x ) = \frac { x } { 3 }$ 
E)  $g ( x ) = \frac { 1 } { 8 } x - 3$

Question 15

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 16

Determine the domain and range of the inverse function $f ^ { - 1 }$ of the following function $f$
$f ( x ) = - | x + 7 | - 1$, where $x > - 7$

Accepted Answer

A)  Domain: $[ - 7 , \infty )$; Range: $[ - 1 , \infty )$ 
B)  Domain: $( - \infty , - 1 ]$; Range: $[ - 7 , \infty )$ 
C)  Domain: $[ - 7 , - 1 ]$; Range: $[ - 7 , \infty )$ 
D)  Domain: $( - \infty , - 7 ]$; Range: $[ 1 , \infty )$ 
E)  Domain: $( - \infty , \infty )$; Range: $( - \infty , \infty )$ 
A)  Domain: $[ - 7 , \infty )$; Range: $[ - 1 , \infty )$ 
B)  Domain: $( - \infty , - 1 ]$; Range: $[ - 7 , \infty )$ 
C)  Domain: $[ - 7 , - 1 ]$; Range: $[ - 7 , \infty )$ 
D)  Domain: $( - \infty , - 7 ]$; Range: $[ 1 , \infty )$ 
E)  Domain: $( - \infty , \infty )$; Range: $( - \infty , \infty )$

Question 17

The scatter plots of different data are shown below. Determine whether there is a positive correlation, negative correlation, or no discernible correlation between the
Variables.

Accepted Answer

A)  positive correlation 
B)  negative correlation 
C)  no discernible correlation 
A)  positive correlation 
B)  negative correlation 
C)  no discernible correlation

Question 18

Algebraically determine whether the function below is even, odd, or neither.
$f ( q ) = 2 q ^ { 3 / 2 }$

Accepted Answer

A)  even 
B)  odd 
C)  cannot be determined 
D)  neither 
A)  even 
B)  odd 
C)  cannot be determined 
D)  neither

Question 19

Show algebraically that the functions $f$ and $g$ shown below are inverse functions.
$f ( x ) = - \frac { 5 } { 7 } x - 3 , \quad g ( x ) = - \frac { 7 x + 21 } { 5 }$

Accepted Answer

A) $\begin{aligned}
f(g(x)) &=-\frac{5}{7}\left(\frac{7 x+21}{5}\right)-3 \
&=\left(\frac{7 x+21}{7}\right)-3 \
&=(x+3)-3 \
&=x+3-3 \
&=x
\end{aligned}$

$\begin{aligned}
g(f(x)) &=-\frac{7\left(-\frac{5}{7} x-3\right)+21}{5} \\
&=-\frac{(-5 x-21)+21}{5} \\
&=\frac{-5 x-21+21}{5} \\
&=\frac{5 x}{5} \\
&=\quad \frac{x}{x}
\end{aligned}$ 
B) $\begin{aligned}
f(g(x)) &=-\frac{5}{7}\left(-\frac{7 x+21}{5}\right)-21 \
&=\left(\frac{35 x+21}{35}\right)-21 \
&=(x+21)-21 \
&=x+21-21 \
&=x
\end{aligned}$

$\begin{aligned}
g(f(x)) &=-\frac{7\left(-\frac{5}{7} x-3\right)+21}{5} \
&=-\frac{(-5 x-3)+21}{5} \
&=\frac{5 x+3-21}{5} \
&=\quad \frac{5 x}{5} \
&=\quad \quad x
\end{aligned}$ 
C) $\begin{array}{rlrl}
f(g(x)) & =-\frac{5}{7}\left(-\frac{7 x+3}{5}\right)-3 & g(f(x)) & =-\frac{7\left(-\frac{5}{7} x-3\right)+21}{5} \\
& =\left(\frac{35 x+3}{35}\right)-3 & & =-\frac{(-5 x-3)+3}{5} \\
& =(x+3)-3 & & =\frac{5 x+3-3}{5} \\
& =x+3-3 & & =\frac{5 x}{5} \\
& =x & & =x
\end{array}$ 
D) $\begin{aligned}
f(g(x)) &=-\frac{5}{7}\left(-\frac{7 x+21}{5}\right)-3 \
&=\left(\frac{7 x+21}{7}\right)-3 \
&=(x+3)-3 \
&=x+3-3 \
&=x
\end{aligned}$

$\begin{aligned}
g(f(x)) &=-\frac{7\left(-\frac{5}{7} x-3\right)+21}{5} \
&=-\frac{(-5 x-21)+21}{5} \
&=\frac{5 x+21-21}{5} \
&=\quad \frac{5 x}{5} \
&=x
\end{aligned}$ 
E) $\begin{aligned}
f(g(x)) &=-\frac{7}{5}\left(-\frac{5 x+15}{7}\right)-3 \
&=\left(\frac{5 x+15}{5}\right)-3 \
&=(x+3)-3 \
&=x+3-3 \
&=x
\end{aligned}$

$\begin{aligned}
g(f(x)) &=-\frac{7\left(-\frac{5}{7} x-3\right)+21}{5} \
&=-\frac{(-5 x-3)+21}{35} \
&=\quad \frac{5 x+3-21}{35} \
&=\quad \frac{35 x}{35} \
&=x
\end{aligned}$ 
A) $\begin{aligned}
f(g(x)) &=-\frac{5}{7}\left(\frac{7 x+21}{5}\right)-3 \
&=\left(\frac{7 x+21}{7}\right)-3 \
&=(x+3)-3 \
&=x+3-3 \
&=x
\end{aligned}$

$\begin{aligned}
g(f(x)) &=-\frac{7\left(-\frac{5}{7} x-3\right)+21}{5} \\
&=-\frac{(-5 x-21)+21}{5} \\
&=\frac{-5 x-21+21}{5} \\
&=\frac{5 x}{5} \\
&=\quad \frac{x}{x}
\end{aligned}$ 
B) $\begin{aligned}
f(g(x)) &=-\frac{5}{7}\left(-\frac{7 x+21}{5}\right)-21 \
&=\left(\frac{35 x+21}{35}\right)-21 \
&=(x+21)-21 \
&=x+21-21 \
&=x
\end{aligned}$

$\begin{aligned}
g(f(x)) &=-\frac{7\left(-\frac{5}{7} x-3\right)+21}{5} \
&=-\frac{(-5 x-3)+21}{5} \
&=\frac{5 x+3-21}{5} \
&=\quad \frac{5 x}{5} \
&=\quad \quad x
\end{aligned}$ 
C) $\begin{array}{rlrl}
f(g(x)) & =-\frac{5}{7}\left(-\frac{7 x+3}{5}\right)-3 & g(f(x)) & =-\frac{7\left(-\frac{5}{7} x-3\right)+21}{5} \\
& =\left(\frac{35 x+3}{35}\right)-3 & & =-\frac{(-5 x-3)+3}{5} \\
& =(x+3)-3 & & =\frac{5 x+3-3}{5} \\
& =x+3-3 & & =\frac{5 x}{5} \\
& =x & & =x
\end{array}$ 
D) $\begin{aligned}
f(g(x)) &=-\frac{5}{7}\left(-\frac{7 x+21}{5}\right)-3 \
&=\left(\frac{7 x+21}{7}\right)-3 \
&=(x+3)-3 \
&=x+3-3 \
&=x
\end{aligned}$

$\begin{aligned}
g(f(x)) &=-\frac{7\left(-\frac{5}{7} x-3\right)+21}{5} \
&=-\frac{(-5 x-21)+21}{5} \
&=\frac{5 x+21-21}{5} \
&=\quad \frac{5 x}{5} \
&=x
\end{aligned}$ 
E) $\begin{aligned}
f(g(x)) &=-\frac{7}{5}\left(-\frac{5 x+15}{7}\right)-3 \
&=\left(\frac{5 x+15}{5}\right)-3 \
&=(x+3)-3 \
&=x+3-3 \
&=x
\end{aligned}$

$\begin{aligned}
g(f(x)) &=-\frac{7\left(-\frac{5}{7} x-3\right)+21}{5} \
&=-\frac{(-5 x-3)+21}{35} \
&=\quad \frac{5 x+3-21}{35} \
&=\quad \frac{35 x}{35} \
&=x
\end{aligned}$

Question 20

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

Write the slope-intercept form of the equation of the line through the given point parallel to the given line. point: $( 3 , - 4 ) \quad$ line: $28 x + 7 y = - 4$

Use the graphs of $y = f ( x )$ and $y = g ( x )$ to evaluate $\left( g ^ { - 1 } \circ f ^ { - 1 } \right) ( - 4 )$ $Use the graphs of y = f ( x ) and y = g ( x ) to evaluate \left( g ^ { - 1 } \circ f ^ { - 1 } \right) ( - 4 )$

Compare the graph of the following function with the graph of $f ( x ) = | x |$ . $y = \left| \frac { 3 } { 4 } x \right|$

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

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

Use function notation to write $g$ in terms of $f ( x ) = \sqrt { x }$ . $g ( x ) = - \frac { 1 } { 3 } \sqrt { x - 8 } + 7$

Determine the domain of $g ( x ) = \frac { 1 } { x ^ { 2 } - 81 }$ .

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

Determine whether lines $L _ { 1 }$ and $L _ { 2 }$ passing through the pairs of points are parallel, perpendicular, or neither. $L _ { 1 } : ( 7 , - 4 ) , ( - 9 , - 1 )$ $L _ { 2 } : ( 4 , - 6 ) , ( - 3,9 )$

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

Find the inverse function of $f$ . $f ( x ) = x ^ { 5 } + 5$

Find $( f g ) ( x )$ $f ( x ) = \sqrt { - 5 x } \quad g ( x ) = \sqrt { - 8 x + 6 }$

Find the inverse function of $f ( x ) = 8 x + 3$

Estimate the slope of the line.

Determine the domain and range of the inverse function $f ^ { - 1 }$ of the following function $f$ $f ( x ) = - | x + 7 | - 1$ , where $x > - 7$

The scatter plots of different data are shown below. Determine whether there is a positive correlation, negative correlation, or no discernible correlation between the Variables.

Algebraically determine whether the function below is even, odd, or neither. $f ( q ) = 2 q ^ { 3 / 2 }$

Show algebraically that the functions $f$ and $g$ shown below are inverse functions. $f ( x ) = - \frac { 5 } { 7 } x - 3 , \quad g ( x ) = - \frac { 7 x + 21 } { 5 }$

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

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

Write the slope-intercept form of the equation of the line through the given point parallel to the given line. point: (3,−4)( 3 , - 4 ) \quad(3,−4) line: 28x+7y=−428 x + 7 y = - 428x+7y=−4

Use the graphs of y=f(x)y = f ( x )y=f(x) and y=g(x)y = g ( x )y=g(x) to evaluate (g−1∘f−1)(−4)\left( g ^ { - 1 } \circ f ^ { - 1 } \right) ( - 4 )(g−1∘f−1)(−4)

Compare the graph of the following function with the graph of f(x)=∣x∣f ( x ) = | x |f(x)=∣x∣ . y=∣34x∣y = \left| \frac { 3 } { 4 } x \right|y=​43​x​

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

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

Use function notation to write ggg in terms of f(x)=xf ( x ) = \sqrt { x }f(x)=x​ . g(x)=−13x−8+7g ( x ) = - \frac { 1 } { 3 } \sqrt { x - 8 } + 7g(x)=−31​x−8​+7

Determine the domain of g(x)=1x2−81g ( x ) = \frac { 1 } { x ^ { 2 } - 81 }g(x)=x2−811​ .

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

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

Find the inverse function of fff . f(x)=x5+5f ( x ) = x ^ { 5 } + 5f(x)=x5+5

Find (fg)(x)( f g ) ( x )(fg)(x) f(x)=−5xg(x)=−8x+6f ( x ) = \sqrt { - 5 x } \quad g ( x ) = \sqrt { - 8 x + 6 }f(x)=−5x​g(x)=−8x+6​

Find the inverse function of f(x)=8x+3f ( x ) = 8 x + 3f(x)=8x+3

Estimate the slope of the line.

Determine the domain and range of the inverse function f−1f ^ { - 1 }f−1 of the following function fff f(x)=−∣x+7∣−1f ( x ) = - | x + 7 | - 1f(x)=−∣x+7∣−1 , where x>−7x > - 7x>−7

The scatter plots of different data are shown below. Determine whether there is a positive correlation, negative correlation, or no discernible correlation between the Variables.

Algebraically determine whether the function below is even, odd, or neither. f(q)=2q3/2f ( q ) = 2 q ^ { 3 / 2 }f(q)=2q3/2

Show algebraically that the functions fff and ggg shown below are inverse functions. f(x)=−57x−3,g(x)=−7x+215f ( x ) = - \frac { 5 } { 7 } x - 3 , \quad g ( x ) = - \frac { 7 x + 21 } { 5 }f(x)=−75​x−3,g(x)=−57x+21​

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

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

Write the slope-intercept form of the equation of the line through the given point parallel to the given line. point: $( 3 , - 4 ) \quad$ line: $28 x + 7 y = - 4$

Use the graphs of $y = f ( x )$ and $y = g ( x )$ to evaluate $\left( g ^ { - 1 } \circ f ^ { - 1 } \right) ( - 4 )$ $Use the graphs of y = f ( x ) and y = g ( x ) to evaluate \left( g ^ { - 1 } \circ f ^ { - 1 } \right) ( - 4 )$

Compare the graph of the following function with the graph of $f ( x ) = | x |$ . $y = \left| \frac { 3 } { 4 } x \right|$

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 function notation to write $g$ in terms of $f ( x ) = \sqrt { x }$ . $g ( x ) = - \frac { 1 } { 3 } \sqrt { x - 8 } + 7$

Determine the domain of $g ( x ) = \frac { 1 } { x ^ { 2 } - 81 }$ .

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

Find the inverse function of $f$ . $f ( x ) = x ^ { 5 } + 5$

Find $( f g ) ( x )$ $f ( x ) = \sqrt { - 5 x } \quad g ( x ) = \sqrt { - 8 x + 6 }$

Find the inverse function of $f ( x ) = 8 x + 3$

Determine the domain and range of the inverse function $f ^ { - 1 }$ of the following function $f$ $f ( x ) = - | x + 7 | - 1$ , where $x > - 7$

Algebraically determine whether the function below is even, odd, or neither. $f ( q ) = 2 q ^ { 3 / 2 }$

Show algebraically that the functions $f$ and $g$ shown below are inverse functions. $f ( x ) = - \frac { 5 } { 7 } x - 3 , \quad g ( x ) = - \frac { 7 x + 21 } { 5 }$

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