Question 1

$\text { Use the functions } f ( x ) = x + 2 \text { and } g ( x ) = 4 x - 3 \text { to find the function } ( f \circ g ) ^ { - 1 } ( x ) \text {. }$

Accepted Answer

A)  $4 x - 5$ 
B)  $\frac { x - 5 } { 4 }$ 
C)  $\frac { x + 1 } { 4 }$ 
D)  $\frac { x - 1 } { 3 }$ 
E)  $4 x + 1$ 
A)  $4 x - 5$ 
B)  $\frac { x - 5 } { 4 }$ 
C)  $\frac { x + 1 } { 4 }$ 
D)  $\frac { x - 1 } { 3 }$ 
E)  $4 x + 1$

Question 2

Solve the following equation for . $\ln ( x - 5 ) ^ { 5 } = 3$

Accepted Answer

A)  $x = 8$ 
B) $x = e ^ { \sqrt [ 5 ] { 3 } } + 5$ 
C)  $x = \frac { 3 } { \ln ( 5 ) ^ { 5 } }$ 
D) $x = e ^ { \frac { 3 } { 5 } } + 5$ 
E)  no solution 
A)  $x = 8$ 
B) $x = e ^ { \sqrt [ 5 ] { 3 } } + 5$ 
C)  $x = \frac { 3 } { \ln ( 5 ) ^ { 5 } }$ 
D) $x = e ^ { \frac { 3 } { 5 } } + 5$ 
E)  no solution

Question 3

V8 car engine is coupled to a dynamometer and the horsepower y is measured at different engine speeds $x$ (in thousands of revolutions per minute). The results are shown in the table below. Use a graphing utility to plot the data and graph the cubic model.
$\begin{array}{|c|c|c|c|c|c|c|}
\hline x & 1 & 2 & 3 & 4 & 5 & 6 \
\hline y & 110 & 155 & 210 & 270 & 295 & 315 \
\hline
\end{array}$

Accepted Answer

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

Question 4

$\text { Find } f ^ { - 1 } ( x ) \text { if } f ( x ) = x ^ { 7 }$

Accepted Answer

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

Question 5

$\text { Specify a sequence of transformations for the function } h ( x ) = \sin \left( x + \frac { \pi } { 3 } \right) + 7 \text { that }$ will yield the graph of $h$ from the graph of the function $f ( x ) = \sin x$.

Accepted Answer

A) 
The function $h ( x ) = \sin \left( x + \frac { \pi } { 3 } \right) + 7$ is a horizontal shift $\frac { \pi } { 3 }$ units to the right, followed by a vertical shift 7 units downwards. 
B)  The function $h ( x ) = \sin \left( x + \frac { \pi } { 3 } \right) + 7$ is a horizontal shift $\frac { \pi } { 3 }$ units to the left, followed by a vertical shift 7 units upwards. 
C)  The function $h ( x ) = \sin \left( x + \frac { \pi } { 3 } \right) + 7$ is a horizontal shift $\frac { \pi } { 3 }$ units to the left, followed by a horizontal shift 7 units to the right. 
D)  The function $h ( x ) = \sin \left( x + \frac { \pi } { 3 } \right) + 7$ is a vertical shift $\frac { \pi } { 3 }$ units downwards, followed by a horizontal shift 7 units to the right. 
E)  The function $h ( x ) = \sin \left( x + \frac { \pi } { 3 } \right) + 7$ is a vertical shift $\frac { \pi } { 3 }$ units upwards, followed by a horizontal shift 7 units to the left. 
A) 
The function $h ( x ) = \sin \left( x + \frac { \pi } { 3 } \right) + 7$ is a horizontal shift $\frac { \pi } { 3 }$ units to the right, followed by a vertical shift 7 units downwards. 
B)  The function $h ( x ) = \sin \left( x + \frac { \pi } { 3 } \right) + 7$ is a horizontal shift $\frac { \pi } { 3 }$ units to the left, followed by a vertical shift 7 units upwards. 
C)  The function $h ( x ) = \sin \left( x + \frac { \pi } { 3 } \right) + 7$ is a horizontal shift $\frac { \pi } { 3 }$ units to the left, followed by a horizontal shift 7 units to the right. 
D)  The function $h ( x ) = \sin \left( x + \frac { \pi } { 3 } \right) + 7$ is a vertical shift $\frac { \pi } { 3 }$ units downwards, followed by a horizontal shift 7 units to the right. 
E)  The function $h ( x ) = \sin \left( x + \frac { \pi } { 3 } \right) + 7$ is a vertical shift $\frac { \pi } { 3 }$ units upwards, followed by a horizontal shift 7 units to the left.

Question 6

$\text { Write an equation of the line that passes through the point } ( - 6,4 ) \text { and is }$ perpendicular to the line $x + y = 5$.

Accepted Answer

A)  $x - y + 10 = 0$ 
B)  $x - y + 2 = 0$ 
C)  $x + y - 2 = 0$ 
D)  $x + y + 10 = 0$ 
E)  $x + y - 5 = 0$ 
A)  $x - y + 10 = 0$ 
B)  $x - y + 2 = 0$ 
C)  $x + y - 2 = 0$ 
D)  $x + y + 10 = 0$ 
E)  $x + y - 5 = 0$

Question 7

moving conveyor is built to rise 5 meters for every 7 meters of horizontal change. Find the slope of the conveyor.

Accepted Answer

A)  0 
B)  $\frac { 5 } { 7 }$ 
C)  $\frac { 7 } { 5 }$ 
D)  $- \frac { 7 } { 5 }$ 
E)  $- \frac { 5 } { 7 }$ 
A)  0 
B)  $\frac { 5 } { 7 }$ 
C)  $\frac { 7 } { 5 }$ 
D)  $- \frac { 7 } { 5 }$ 
E)  $- \frac { 5 } { 7 }$

Question 8

$\text { Find } f ^ { - 1 } ( x ) \text { if } f ( x ) = 12 x - 10 \text {. }$

Accepted Answer

A)  $f ^ { - 1 } ( x ) = \ln ( 12 x + 10 )$ 
B)  $f ^ { - 1 } ( x ) = \frac { 1 } { 12 x - 10 }$ 
C)  $f ^ { - 1 } ( x ) = \frac { 1 } { 12 } x + \frac { 1 } { 10 }$ 
D)  $f ^ { - 1 } ( x ) = 10 x - 12$ 
E)  $f ^ { - 1 } ( x ) = \frac { 1 } { 12 } x + \frac { 5 } { 6 }$ 
A)  $f ^ { - 1 } ( x ) = \ln ( 12 x + 10 )$ 
B)  $f ^ { - 1 } ( x ) = \frac { 1 } { 12 x - 10 }$ 
C)  $f ^ { - 1 } ( x ) = \frac { 1 } { 12 } x + \frac { 1 } { 10 }$ 
D)  $f ^ { - 1 } ( x ) = 10 x - 12$ 
E)  $f ^ { - 1 } ( x ) = \frac { 1 } { 12 } x + \frac { 5 } { 6 }$

Question 9

Determine whether y is a function of x. $x y - x ^ { 2 } = 3 y + x$

Accepted Answer

A) True 
 B)False

Question 10

Sketch the graph of the equation: $$y = | x + 2 |$$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
E)  none of the above 
A) 
  
B) 
  
C) 
  
D) 
  
E)  none of the above

Question 11

Students in a lab measured the breaking strength S (in pounds) of wood 2 inches thick, $x$ inches high, and 12 inches long. The results are shown in the table below. Use the regression capabilities of a graphing utility to fit a quadratic model to the data. Round the numerical values in your answer to two decimal places, where applicable.
$\begin{array}{|c|c|c|c|c|c|}
\hline x & 4 & 6 & 8 & 10 & 12 \
\hline S & 2422 & 5512 & 10,362 & 16,302 & 23,912 \
\hline
\end{array}$

Accepted Answer

A)  $S = 170.89 x ^ { 2 } - 209.79 x + 324$ 
B)  $S = 180.89 x ^ { 2 } - 205.79 x + 324$ 
C)  $S = 190.89 x ^ { 2 } + 201.79 x + 331$ 
D)  $S = 170.89 x ^ { 2 } - 209.79 x + 327$ 
E)  $S = 180.89 x ^ { 2 } + 203.79 x - 331$ 
A)  $S = 170.89 x ^ { 2 } - 209.79 x + 324$ 
B)  $S = 180.89 x ^ { 2 } - 205.79 x + 324$ 
C)  $S = 190.89 x ^ { 2 } + 201.79 x + 331$ 
D)  $S = 170.89 x ^ { 2 } - 209.79 x + 327$ 
E)  $S = 180.89 x ^ { 2 } + 203.79 x - 331$

Question 12

Solve the following equation for . $\arcsin ( 7 x - \pi ) = \frac { 1 } { 10 }$

Accepted Answer

A)  $x = \frac { \pi + \sin \left( \frac { 1 } { 10 } \right) } { 7 }$ 
B)  $x = \frac { \cos \left( \pi + \frac { 1 } { 10 } \right) } { 7 }$ 
C)  $x = \frac { \csc \left( \pi + \frac { 1 } { 10 } \right) } { 7 }$ 
D)  $x = \frac { \pi + \csc \left( \frac { 1 } { 10 } \right) } { 7 }$
$x = \frac { \sin \left( \pi + \frac { 1 } { 10 } \right) } { 7 }$ 
A)  $x = \frac { \pi + \sin \left( \frac { 1 } { 10 } \right) } { 7 }$ 
B)  $x = \frac { \cos \left( \pi + \frac { 1 } { 10 } \right) } { 7 }$ 
C)  $x = \frac { \csc \left( \pi + \frac { 1 } { 10 } \right) } { 7 }$ 
D)  $x = \frac { \pi + \csc \left( \frac { 1 } { 10 } \right) } { 7 }$
$x = \frac { \sin \left( \pi + \frac { 1 } { 10 } \right) } { 7 }$

Question 13

$\text { Suppose that the dollar value of a product in } 2008 \text { is } \$ 174 \text { and the rate at which the }$ value of the product is expected to increase per year during the next 5 years is $\$ 7.50$. Write a linear equation that gives the dollar value $V$ of the product in terms of the year $t$. (Let $t = 0$ represent 2000.) Round the numerical values in your answer to one decimal place, where applicable.

Accepted Answer

A)  $V = 7.5 t - 159$ 
B)  $V = - 7.5 t - 114$ 
C)  $V = - 7.5 t + 174$ 
D)  $V = 7.5 t + 114$ 
E)  $V = 7.5 t - 144$ 
A)  $V = 7.5 t - 159$ 
B)  $V = - 7.5 t - 114$ 
C)  $V = - 7.5 t + 174$ 
D)  $V = 7.5 t + 114$ 
E)  $V = 7.5 t - 144$

Question 14

$\text { Find the distance between the point } ( - 4,7 ) \text { and line } x - y - 2 = 0 \text { using the formula, }$ Distance $= \frac { \left| A x _ { 1 } + B y _ { 1 } + C \right| } { \sqrt { A ^ { 2 } + B ^ { 2 } } }$ for the distance between the point $\left( x _ { 1 } , y _ { 1 } \right)$ and the line $A x + B y + C = 0$

Accepted Answer

A)  $\frac { 11 \sqrt { 2 } } { 2 }$ 
B)  $\frac { 4 \sqrt { 3 } } { 3 }$ 
C)  $\frac { 13 \sqrt { 2 } } { 2 }$ 
D)  $\frac { 9 \sqrt { 2 } } { 2 }$ 
E)  $\frac { 6 \sqrt { 3 } } { 3 }$ 
A)  $\frac { 11 \sqrt { 2 } } { 2 }$ 
B)  $\frac { 4 \sqrt { 3 } } { 3 }$ 
C)  $\frac { 13 \sqrt { 2 } } { 2 }$ 
D)  $\frac { 9 \sqrt { 2 } } { 2 }$ 
E)  $\frac { 6 \sqrt { 3 } } { 3 }$

Question 15

Write the following expression as a logarithm of a single quantity. $13 \ln x - 12 \ln \left( x ^ { 2 } + 16 \right)$

Accepted Answer

A)  $\ln \left( 13 x - 12 \left( x ^ { 2 } + 16 \right) \right)$ 
B)  $\ln \left( \frac { x ^ { 13 } } { \left( x ^ { 2 } + 16 \right) ^ { 12 } } \right)$ 
C)  $\ln \left( x ^ { 13 } \left( x ^ { 2 } + 16 \right) ^ { 12 } \right)$ 
D)  $\ln \left( x ^ { 13 } - \left( x ^ { 2 } + 16 \right) ^ { 12 } \right)$ 
E)  $\ln \left( \frac { x ^ { 13 } } { 12 \left( x ^ { 2 } + 16 \right) } \right)$ 
A)  $\ln \left( 13 x - 12 \left( x ^ { 2 } + 16 \right) \right)$ 
B)  $\ln \left( \frac { x ^ { 13 } } { \left( x ^ { 2 } + 16 \right) ^ { 12 } } \right)$ 
C)  $\ln \left( x ^ { 13 } \left( x ^ { 2 } + 16 \right) ^ { 12 } \right)$ 
D)  $\ln \left( x ^ { 13 } - \left( x ^ { 2 } + 16 \right) ^ { 12 } \right)$ 
E)  $\ln \left( \frac { x ^ { 13 } } { 12 \left( x ^ { 2 } + 16 \right) } \right)$

Question 16

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 a measure of the stiffness of the spring and is called the spring constant. The table shows the elongation $d$ in centimeters of a spring when a force of $F$ newtons is applied. Use the model $d = 0.085 F$ to estimate the elongation of the spring when a force of 55 newtons is applied. Round your answer to two decimal places.
$\begin{array}{|c|c|c|c|c|c|}
\hline F & 20 & 40 & 60 & 80 & 100 \
\hline d & 1.7 & 3.4 & 5.1 & 6.8 & 8.5 \
\hline
\end{array}$

Accepted Answer

A)  $8.08 \mathrm {~cm}$ 
B)  $6.38 \mathrm {~cm}$ 
C)  $4.68 \mathrm {~cm}$ 
D)  $2.98 \mathrm {~cm}$ 
E)  $9.78 \mathrm {~cm}$ 
A)  $8.08 \mathrm {~cm}$ 
B)  $6.38 \mathrm {~cm}$ 
C)  $4.68 \mathrm {~cm}$ 
D)  $2.98 \mathrm {~cm}$ 
E)  $9.78 \mathrm {~cm}$

Question 17

$\text { Solve the following equation for } x \text {. }$ $e ^ { \ln ( 13 x ) } = 3$

Accepted Answer

A)  $x = \frac { \ln ( 3 ) } { \ln ( 13 ) }$ 
B)  $x = \frac { 3 } { 13 }$ 
C)  $x = 39$ 
D)  $x = \frac { 3 } { \ln ( 13 ) }$ 
E)  $x = \frac { 3 } { e \ln ( 13 ) }$ 
A)  $x = \frac { \ln ( 3 ) } { \ln ( 13 ) }$ 
B)  $x = \frac { 3 } { 13 }$ 
C)  $x = 39$ 
D)  $x = \frac { 3 } { \ln ( 13 ) }$ 
E)  $x = \frac { 3 } { e \ln ( 13 ) }$

Question 18

$\text { Find the domain and range of the function } f ( x ) = x ^ { 2 } - 6 \text {. }$

Accepted Answer

A)  domain: $[ - 6 , \infty )$
range: $[ - 6 , \infty )$ 
B)  domain: $[ - 6 , \infty )$
range: $( - 6 , \infty )$ 
C)  domain: $( - \infty , \infty )$
range: $( - 6 , \infty )$ 
D)  domain: $( - \infty , \infty )$
range: $[ 6 , \infty )$ 
E)  domain: $( - \infty , \infty )$
range: $[ - 6 , \infty )$ 
A)  domain: $[ - 6 , \infty )$
range: $[ - 6 , \infty )$ 
B)  domain: $[ - 6 , \infty )$
range: $( - 6 , \infty )$ 
C)  domain: $( - \infty , \infty )$
range: $( - 6 , \infty )$ 
D)  domain: $( - \infty , \infty )$
range: $[ 6 , \infty )$ 
E)  domain: $( - \infty , \infty )$
range: $[ - 6 , \infty )$

Question 19

the points of intersection of the graphs of the equations: 
$\begin{array} { l } 
x = y ^ { 2 } - 3 \
y = x + 1
\end{array}$

Accepted Answer

A)  $( - 2,1 ) , ( - 1,2 )$ 
B)  $( - 2,0 ) , ( 1,2 )$ 
C)  $( - 2 , - 1 ) , ( 1,2 )$ 
D)  $( 2 , - 1 ) , ( - 1,2 )$ 
E)  $( - 2 , - 3 ) , ( - 1,2 )$ 
A)  $( - 2,1 ) , ( - 1,2 )$ 
B)  $( - 2,0 ) , ( 1,2 )$ 
C)  $( - 2 , - 1 ) , ( 1,2 )$ 
D)  $( 2 , - 1 ) , ( - 1,2 )$ 
E)  $( - 2 , - 3 ) , ( - 1,2 )$

Question 20

In an experiment, students measured the speed s (in meters per second) of a falling object $t$ seconds after it was released. The results are shown in the table below. Use the model $s = 11.9 t + 4.8$ to estimate the speed of the object after $1.5$ seconds. Round your answer to two decimal places.
$\begin{array}{|c|c|c|c|c|c|}
\hline t & 0 & 1 & 2 & 3 & 4 \
\hline s & 0 & 22.0 & 30.4 & 40.2 & 50.4 \
\hline
\end{array}$

Accepted Answer

A)  $21.05$ meters/second 
B)  $20.95 \mathrm {~meters} / \mathrm { second }$ 
C)  $24.25 \mathrm {~meters} / \mathrm { second }$ 
D)  $23.55$ meters/second 
E)  $22.65$ meters/second 
A)  $21.05$ meters/second 
B)  $20.95 \mathrm {~meters} / \mathrm { second }$ 
C)  $24.25 \mathrm {~meters} / \mathrm { second }$ 
D)  $23.55$ meters/second 
E)  $22.65$ meters/second

$\text { Use the functions } f ( x ) = x + 2 \text { and } g ( x ) = 4 x - 3 \text { to find the function } ( f \circ g ) ^ { - 1 } ( x ) \text {. }$

Solve the following equation for . $\ln ( x - 5 ) ^ { 5 } = 3$

V8 car engine is coupled to a dynamometer and the horsepower y is measured at different engine speeds $x$ (in thousands of revolutions per minute). The results are shown in the table below. Use a graphing utility to plot the data and graph the cubic model. x 1 2 3 4 5 6 y 110 155 210 270 295 315

$\text { Find } f ^ { - 1 } ( x ) \text { if } f ( x ) = x ^ { 7 }$

$\text { Specify a sequence of transformations for the function } h ( x ) = \sin \left( x + \frac { \pi } { 3 } \right) + 7 \text { that }$ will yield the graph of $h$ from the graph of the function $f ( x ) = \sin x$ .

$\text { Write an equation of the line that passes through the point } ( - 6,4 ) \text { and is }$ perpendicular to the line $x + y = 5$ .

moving conveyor is built to rise 5 meters for every 7 meters of horizontal change. Find the slope of the conveyor.

$\text { Find } f ^ { - 1 } ( x ) \text { if } f ( x ) = 12 x - 10 \text {. }$

Determine whether y is a function of x. $x y - x ^ { 2 } = 3 y + x$

Sketch the graph of the equation: $y = | x + 2 |$

Solve the following equation for . $\arcsin ( 7 x - \pi ) = \frac { 1 } { 10 }$

Write the following expression as a logarithm of a single quantity. $13 \ln x - 12 \ln \left( x ^ { 2 } + 16 \right)$

$\text { Solve the following equation for } x \text {. }$ $e ^ { \ln ( 13 x ) } = 3$

$\text { Find the domain and range of the function } f ( x ) = x ^ { 2 } - 6 \text {. }$

the points of intersection of the graphs of the equations: x=-3 y=x+1

A Preview of Calculus

The Derivative and the Tangent Line Problem

Extrema on an Interval

Antiderivatives and Indefinite Integration

Slope Fields and Eulers Method

Area of a Region Between Two Curves

Basic Integration Rules

Sequences

Conics and Calculus

Vectors in the Plane

Vector-Valued Functions

Introduction to Functions of Several Variables

Iterated Integrals and Area in the Plane

Vector Fields

Exact First-Order Equations

Filters

Exam 1: Graphs and Models

Solve the following equation for . ln⁡(x−5)5=3\ln ( x - 5 ) ^ { 5 } = 3ln(x−5)5=3

V8 car engine is coupled to a dynamometer and the horsepower y is measured at different engine speeds xxx (in thousands of revolutions per minute). The results are shown in the table below. Use a graphing utility to plot the data and graph the cubic model. x 1 2 3 4 5 6 y 110 155 210 270 295 315

Find f−1(x) if f(x)=x7\text { Find } f ^ { - 1 } ( x ) \text { if } f ( x ) = x ^ { 7 } Find f−1(x) if f(x)=x7

Write an equation of the line that passes through the point (−6,4) and is \text { Write an equation of the line that passes through the point } ( - 6,4 ) \text { and is } Write an equation of the line that passes through the point (−6,4) and is perpendicular to the line x+y=5x + y = 5x+y=5 .

moving conveyor is built to rise 5 meters for every 7 meters of horizontal change. Find the slope of the conveyor.

Find f−1(x) if f(x)=12x−10. \text { Find } f ^ { - 1 } ( x ) \text { if } f ( x ) = 12 x - 10 \text {. } Find f−1(x) if f(x)=12x−10.

Determine whether y is a function of x. xy−x2=3y+xx y - x ^ { 2 } = 3 y + xxy−x2=3y+x

Sketch the graph of the equation: y=∣x+2∣y = | x + 2 |y=∣x+2∣

Solve the following equation for . arcsin⁡(7x−π)=110\arcsin ( 7 x - \pi ) = \frac { 1 } { 10 }arcsin(7x−π)=101​

Write the following expression as a logarithm of a single quantity. 13ln⁡x−12ln⁡(x2+16)13 \ln x - 12 \ln \left( x ^ { 2 } + 16 \right)13lnx−12ln(x2+16)

Solve the following equation for x. \text { Solve the following equation for } x \text {. } Solve the following equation for x. eln⁡(13x)=3e ^ { \ln ( 13 x ) } = 3eln(13x)=3

Find the domain and range of the function f(x)=x2−6. \text { Find the domain and range of the function } f ( x ) = x ^ { 2 } - 6 \text {. } Find the domain and range of the function f(x)=x2−6.

the points of intersection of the graphs of the equations: x=-3 y=x+1

A Preview of Calculus

The Derivative and the Tangent Line Problem

Extrema on an Interval

Antiderivatives and Indefinite Integration

Slope Fields and Eulers Method

Area of a Region Between Two Curves

Basic Integration Rules

Sequences

Conics and Calculus

Vectors in the Plane

Vector-Valued Functions

Introduction to Functions of Several Variables

Iterated Integrals and Area in the Plane

Vector Fields

Exact First-Order Equations

Filters

Solve the following equation for . $\ln ( x - 5 ) ^ { 5 } = 3$

V8 car engine is coupled to a dynamometer and the horsepower y is measured at different engine speeds $x$ (in thousands of revolutions per minute). The results are shown in the table below. Use a graphing utility to plot the data and graph the cubic model. x 1 2 3 4 5 6 y 110 155 210 270 295 315

$\text { Find } f ^ { - 1 } ( x ) \text { if } f ( x ) = x ^ { 7 }$

$\text { Write an equation of the line that passes through the point } ( - 6,4 ) \text { and is }$ perpendicular to the line $x + y = 5$ .

$\text { Find } f ^ { - 1 } ( x ) \text { if } f ( x ) = 12 x - 10 \text {. }$

Determine whether y is a function of x. $x y - x ^ { 2 } = 3 y + x$

Sketch the graph of the equation: $y = | x + 2 |$

Solve the following equation for . $\arcsin ( 7 x - \pi ) = \frac { 1 } { 10 }$

Write the following expression as a logarithm of a single quantity. $13 \ln x - 12 \ln \left( x ^ { 2 } + 16 \right)$

$\text { Solve the following equation for } x \text {. }$ $e ^ { \ln ( 13 x ) } = 3$

$\text { Find the domain and range of the function } f ( x ) = x ^ { 2 } - 6 \text {. }$