Question 1

$\text { Determine the domain and range of the function } f ( x ) = \left\{ \begin{array} { l } 
3 x + 2 , x < 0 \
3 x + 6 , x \geq 0
\end{array} \right. \text {. }$

Accepted Answer

A)  domain: $( - \infty , 2 )$
range: $( - \infty , 2 ) \cap [ 6 , \infty ]$ 
B)  domain: $( - \infty , \infty )$
range: $( - \infty , 2 ) \cup [ 6 , \infty )$ 
C)  domain: $( - \infty , \infty )$
range: $( - \infty , 2 ) \cup ( \infty , 6 ]$ 
D)  domain: $( - \infty , \infty )$
range: $( \infty , 2 ) \cup ( 6 , - \infty )$ 
E)  domain: $( - \infty , 3 )$
range: $( - \infty , 2 ) \cap [ 6 , \infty )$ 
A)  domain: $( - \infty , 2 )$
range: $( - \infty , 2 ) \cap [ 6 , \infty ]$ 
B)  domain: $( - \infty , \infty )$
range: $( - \infty , 2 ) \cup [ 6 , \infty )$ 
C)  domain: $( - \infty , \infty )$
range: $( - \infty , 2 ) \cup ( \infty , 6 ]$ 
D)  domain: $( - \infty , \infty )$
range: $( \infty , 2 ) \cup ( 6 , - \infty )$ 
E)  domain: $( - \infty , 3 )$
range: $( - \infty , 2 ) \cap [ 6 , \infty )$

Question 2

all intercepts: $$y = 64 x - x ^ { 3 }$$

Accepted Answer

A)  $x$-intercepts: $( - 8,0 ) , ( 8,0 )$; no $y$-intercept 
B)  $x$-intercept: $( 0,0 ) ; y$-intercepts: $( 0,0 ) , ( 0 , - 8 ) , ( 0,8 )$ 
C)  $x$-intercepts: $( 0,0 ) , ( - 8,0 ) , ( 8,0 ) ; y$-intercept: $( 0,0 )$ 
D)  $x$-intercepts: $( 0,0 ) , ( - 8,0 ) , ( 8,0 )$; no $y$-intercept 
E)  $x$-intercepts: $( - 8,0 ) , 8 ; y$-intercept: $( 0,0 )$ 
A)  $x$-intercepts: $( - 8,0 ) , ( 8,0 )$; no $y$-intercept 
B)  $x$-intercept: $( 0,0 ) ; y$-intercepts: $( 0,0 ) , ( 0 , - 8 ) , ( 0,8 )$ 
C)  $x$-intercepts: $( 0,0 ) , ( - 8,0 ) , ( 8,0 ) ; y$-intercept: $( 0,0 )$ 
D)  $x$-intercepts: $( 0,0 ) , ( - 8,0 ) , ( 8,0 )$; no $y$-intercept 
E)  $x$-intercepts: $( - 8,0 ) , 8 ; y$-intercept: $( 0,0 )$

Question 3

Use the Horizontal Line Test to determine whether the following statement is true or false. The function $f ( x ) = 14 ( x - 15 ) + 15$ is one-to-one on its entire domain and therefore has an inverse function.

Accepted Answer

A) True 
 B)False

Question 4

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 regression capabilities of a graphing utility to find a linear model for the data. Round all numerical values in your answer to one decimal place.
$\begin{array}{|c|c|c|c|c|c|}
\hline t & 0 & 1 & 2 & 3 & 4 \
\hline s & 0 & 13.0 & 21.4 & 31.2 & 41.4 \
\hline
\end{array}$

Accepted Answer

A)  $s = 10.1 t + 1.2$ 
B)  $s = 3.0 t - 1.2$ 
C)  $s = 1.2 t + 10.1$ 
D)  $s = 10.1 t + 3.0$ 
E)  $s = 1.2 t - 3.0$ 
A)  $s = 10.1 t + 1.2$ 
B)  $s = 3.0 t - 1.2$ 
C)  $s = 1.2 t + 10.1$ 
D)  $s = 10.1 t + 3.0$ 
E)  $s = 1.2 t - 3.0$

Question 5

$\text { Find the sales necessary to break even } ( R = C ) \text { if the cost } C \text { of producing } x \text { units is }$ $C = 5.3 \sqrt { x } + 40,000$ and the revenue $R$ for selling $x$ units is $R = 3.3 x$. Round your answer to the nearest integer.

Accepted Answer

A)  $\quad x \approx 6,244$ units 
B)  $x \approx 12,334$ units 
C)  $x \approx 12,305$ units 
D)  $x \approx 12,299$ units 
E)  $x \approx 6,239$ units 
A)  $\quad x \approx 6,244$ units 
B)  $x \approx 12,334$ units 
C)  $x \approx 12,305$ units 
D)  $x \approx 12,299$ units 
E)  $x \approx 6,239$ units

Question 6

Write the following expression as a logarithm of a single quantity. $\ln x - 4 \ln \left( x ^ { 2 } + 1 \right)$

Accepted Answer

A)  $\ln \left( \frac { x } { \left( x ^ { 2 } + 1 \right) ^ { - 4 } } \right)$ 
B)  $\ln \left( x - 4 \left( x ^ { 2 } + 1 \right) \right)$ 
C)  $\ln \left( \frac { x } { 4 \left( x ^ { 2 } + 1 \right) } \right)$ 
D)  $\ln \left( \frac { - 4 x } { x ^ { 2 } + 1 } \right)$ 
E)  $\ln \left( \frac { x } { \left( x ^ { 2 } + 1 \right) ^ { 4 } } \right)$ 
A)  $\ln \left( \frac { x } { \left( x ^ { 2 } + 1 \right) ^ { - 4 } } \right)$ 
B)  $\ln \left( x - 4 \left( x ^ { 2 } + 1 \right) \right)$ 
C)  $\ln \left( \frac { x } { 4 \left( x ^ { 2 } + 1 \right) } \right)$ 
D)  $\ln \left( \frac { - 4 x } { x ^ { 2 } + 1 } \right)$ 
E)  $\ln \left( \frac { x } { \left( x ^ { 2 } + 1 \right) ^ { 4 } } \right)$

Question 7

You need 50 pounds of two commodities costing $1.80 and $2.40 per pound. Find the inverse function of the cost function $y = 1.80 x + 2.40 ( 50 - x )$.

Accepted Answer

A)  $y = \frac { 5 } { 3 } ( 240 - x )$ 
B)  $y = \frac { 10 } { 3 } ( - 120 + x )$ 
C) $y = \frac { 5 } { 3 } ( - 240 - x )$ 
D)  $y = \frac { 5 } { 3 } ( 120 - x )$ 
E)  $y = \frac { 10 } { 3 } ( 120 + x )$ 
A)  $y = \frac { 5 } { 3 } ( 240 - x )$ 
B)  $y = \frac { 10 } { 3 } ( - 120 + x )$ 
C) $y = \frac { 5 } { 3 } ( - 240 - x )$ 
D)  $y = \frac { 5 } { 3 } ( 120 - x )$ 
E)  $y = \frac { 10 } { 3 } ( 120 + x )$

Question 8

$$\text { What is the domain of the function } f ( x ) = 4 + \ln ( x - 6 ) ?$$

Accepted Answer

A)  $( 1 , \infty )$ 
B)  $( 6 , \infty )$ 
C)  $( 0 , \infty )$ 
D)  $( 0,6 )$ 
E)  $( 1,6 )$ 
A)  $( 1 , \infty )$ 
B)  $( 6 , \infty )$ 
C)  $( 0 , \infty )$ 
D)  $( 0,6 )$ 
E)  $( 1,6 )$

Question 9

$\text { Evaluate (if possible) the function } f ( x ) = - 6 x - 5 \text { at } x = - 2 \text {. Simplify the result. }$

Accepted Answer

A)  $- 7$ 
B)  17 
C)  3 
D)  7 
E)  undefined 
A)  $- 7$ 
B)  17 
C)  3 
D)  7 
E)  undefined

Question 10

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 a graphing utility to plot the data and graph the quadratic model.
$\begin{array}{|c|c|c|c|c|c|}
\hline x & 4 & 6 & 8 & 10 & 12 \
\hline S & 2370 & 4460 & 13,310 & 19,250 & 29,860 \
\hline
\end{array}$

Accepted Answer

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

Question 11

$\text { Find } f ^ { - 1 } ( x ) \text { if } f ( x ) = \sqrt { 13 - x ^ { 2 } } , 0 \leq x \leq \sqrt { 13 }$

Accepted Answer

A)  $f ^ { - 1 } ( x ) = x + \sqrt { 13 } , 0 \leq x \leq \sqrt { 13 }$ 
B)  $f ^ { - 1 } ( x ) = \left( 13 - x ^ { 2 } \right) ^ { 2 } , 0 \leq x \leq \sqrt { 13 }$ 
C)  $f ^ { - 1 } ( x ) = \sqrt { 13 - x ^ { 2 } } , 0 \leq x \leq \sqrt { 13 }$ 
D)  $f ^ { - 1 } ( x ) = \sqrt { x ^ { 2 } - 13 } , 0 \leq x \leq \sqrt { 13 }$ 
E)  $f ^ { - 1 } ( x ) = \frac { 1 } { \sqrt { 13 - x ^ { 2 } } } , 0 \leq x \leq \sqrt { 13 }$ 
A)  $f ^ { - 1 } ( x ) = x + \sqrt { 13 } , 0 \leq x \leq \sqrt { 13 }$ 
B)  $f ^ { - 1 } ( x ) = \left( 13 - x ^ { 2 } \right) ^ { 2 } , 0 \leq x \leq \sqrt { 13 }$ 
C)  $f ^ { - 1 } ( x ) = \sqrt { 13 - x ^ { 2 } } , 0 \leq x \leq \sqrt { 13 }$ 
D)  $f ^ { - 1 } ( x ) = \sqrt { x ^ { 2 } - 13 } , 0 \leq x \leq \sqrt { 13 }$ 
E)  $f ^ { - 1 } ( x ) = \frac { 1 } { \sqrt { 13 - x ^ { 2 } } } , 0 \leq x \leq \sqrt { 13 }$

Question 12

$$\text { Which of the following is the correct graph of } y = 2 - x \text { ? }$$

Accepted Answer

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

Question 13

table given below shows the Consumer Price Index (CPI) for selected years. Use a graphing utility to plot the data and graph the model $y = - 0.1476 t ^ { 2 } + 9.6462 t + 3.8286$
$\begin{array}{|c|c|c|c|c|c|c|r|}
\hline \text { ear } & 975 & 980 & 985 & 990 & 995 & 000 & 005 \
\hline \text { PI } & 5.5 & 0.6 & 05.5 & 35.5 & 60.5 & 72.5 & 50.5 \
\hline
\end{array}$

Accepted Answer

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

Question 14

$\text { Evaluate the function } f ( x ) = \left\{ \begin{array} { l } 
2 x + 1 , x < 0 \
2 x + 2 , x \geq 0
\end{array} \text { at } f ( 5 ) \right.$

Accepted Answer

A)  $f ( 5 ) = 6$ 
B)  $f ( 5 ) = 5$ 
C)  $f ( 5 ) = 13$ 
D)  $f ( 5 ) = 11$ 
E)  $f ( 5 ) = 12$ 
A)  $f ( 5 ) = 6$ 
B)  $f ( 5 ) = 5$ 
C)  $f ( 5 ) = 13$ 
D)  $f ( 5 ) = 11$ 
E)  $f ( 5 ) = 12$

Question 15

Sketch the graph of the equation: $$x = 4 - y ^ { 2 }$$

Accepted Answer

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

Question 16

$\text { Sketch a graph of the equation } y - 8 = 2 ( x + 4 ) \text {. }$

Accepted Answer

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

Question 17

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

Accepted Answer

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

Question 18

Table given below shows the Consumer Price Index (CPI) for selected years. Use the regression capabilities of a graphing utility to find a mathematical model of the form $y = a t ^ { 2 } + b t + c$ for the data. In the model, $y$ represents the CPI and $t$ represents the year, with $t = 5$ corresponding to 1975 . Round all numerical values in your answer to three decimal places.
$\begin{array}{|c|c|c|c|c|c|c|c|}
\hline \text { ear } & 975 & 980 & 985 & 990 & 995 & 000 & 005 \
\hline \text { PI } & 7.8 & 0.6 & 03.6 & 30.7 & 52.4 & 70.5 & 92.5 \
\hline
\end{array}$

Accepted Answer

A)  $y = - 0.019 t ^ { 2 } + 5.268 t + 30.871$ 
B)  $y = - 0.019 t ^ { 2 } - 5.957 t + 30.871$ 
C)  $y = - 0.016 t ^ { 2 } - 5.957 t - 30.871$ 
D)  $y = - 0.019 t ^ { 2 } + 5.957 t + 40.871$ 
E)  $y = - 0.016 t ^ { 2 } + 5.268 t + 40.871$ 
A)  $y = - 0.019 t ^ { 2 } + 5.268 t + 30.871$ 
B)  $y = - 0.019 t ^ { 2 } - 5.957 t + 30.871$ 
C)  $y = - 0.016 t ^ { 2 } - 5.957 t - 30.871$ 
D)  $y = - 0.019 t ^ { 2 } + 5.957 t + 40.871$ 
E)  $y = - 0.016 t ^ { 2 } + 5.268 t + 40.871$

Question 19

$\text { Evaluate the expression arccos } \left( \frac { \sqrt { 2 } } { 2 } \right) \text { without using a calculator. }$

Accepted Answer

A)  $\frac { 5 \pi } { 4 }$ 
B)  $\frac { \pi } { 6 }$ 
C)  $\frac { 3 \pi } { 2 }$ 
D)  $\frac { \pi } { 4 }$ 
E)  $\frac { 2 \pi } { 3 }$ 
A)  $\frac { 5 \pi } { 4 }$ 
B)  $\frac { \pi } { 6 }$ 
C)  $\frac { 3 \pi } { 2 }$ 
D)  $\frac { \pi } { 4 }$ 
E)  $\frac { 2 \pi } { 3 }$

Question 20

moving conveyor is built to rise 1 meter for every 5 meters of horizontal change. Suppose the conveyor runs between two floors in a factory. Find the length of the conveyor if the Vertical distance between floors is 10 meters. Round your answer to the nearest meter.

Accepted Answer

A) 61 meters 
B) 39 meters 
C) 51 meters 
D) 50 meters 
E) 41 meters 
A) 61 meters 
B) 39 meters 
C) 51 meters 
D) 50 meters 
E) 41 meters

$\text { Determine the domain and range of the function } f ( x ) = \left\{ \begin{array} { l } 3 x + 2 , x < 0 \\3 x + 6 , x \geq 0\end{array} \right. \text {. }$

all intercepts: $y = 64 x - x ^ { 3 }$

Use the Horizontal Line Test to determine whether the following statement is true or false. The function $f ( x ) = 14 ( x - 15 ) + 15$ is one-to-one on its entire domain and therefore has an inverse function.

$\text { Find the sales necessary to break even } ( R = C ) \text { if the cost } C \text { of producing } x \text { units is }$ $C = 5.3 \sqrt { x } + 40,000$ and the revenue $R$ for selling $x$ units is $R = 3.3 x$ . Round your answer to the nearest integer.

Write the following expression as a logarithm of a single quantity. $\ln x - 4 \ln \left( x ^ { 2 } + 1 \right)$

You need 50 pounds of two commodities costing $1.80 and $2.40 per pound. Find the inverse function of the cost function $y = 1.80 x + 2.40 ( 50 - x )$ .

$\text { What is the domain of the function } f ( x ) = 4 + \ln ( x - 6 ) ?$

$\text { Evaluate (if possible) the function } f ( x ) = - 6 x - 5 \text { at } x = - 2 \text {. Simplify the result. }$

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 a graphing utility to plot the data and graph the quadratic model. x 4 6 8 10 12 S 2370 4460 13,310 19,250 29,860

$\text { Find } f ^ { - 1 } ( x ) \text { if } f ( x ) = \sqrt { 13 - x ^ { 2 } } , 0 \leq x \leq \sqrt { 13 }$

$\text { Which of the following is the correct graph of } y = 2 - x \text { ? }$

table given below shows the Consumer Price Index (CPI) for selected years. Use a graphing utility to plot the data and graph the model $y = - 0.1476 t ^ { 2 } + 9.6462 t + 3.8286$ ear 975 980 985 990 995 000 005 PI 5.5 0.6 05.5 35.5 60.5 72.5 50.5

$\text { Evaluate the function } f ( x ) = \left\{ \begin{array} { l } 2 x + 1 , x < 0 \\2 x + 2 , x \geq 0\end{array} \text { at } f ( 5 ) \right.$

Sketch the graph of the equation: $x = 4 - y ^ { 2 }$

$\text { Sketch a graph of the equation } y - 8 = 2 ( x + 4 ) \text {. }$

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

$\text { Evaluate the expression arccos } \left( \frac { \sqrt { 2 } } { 2 } \right) \text { without using a calculator. }$

moving conveyor is built to rise 1 meter for every 5 meters of horizontal change. Suppose the conveyor runs between two floors in a factory. Find the length of the conveyor if the Vertical distance between floors is 10 meters. Round your answer to the nearest meter.

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

all intercepts: y=64x−x3y = 64 x - x ^ { 3 }y=64x−x3

Use the Horizontal Line Test to determine whether the following statement is true or false. The function f(x)=14(x−15)+15f ( x ) = 14 ( x - 15 ) + 15f(x)=14(x−15)+15 is one-to-one on its entire domain and therefore has an inverse function.

Write the following expression as a logarithm of a single quantity. ln⁡x−4ln⁡(x2+1)\ln x - 4 \ln \left( x ^ { 2 } + 1 \right)lnx−4ln(x2+1)

You need 50 pounds of two commodities costing $1.80 and $2.40 per pound. Find the inverse function of the cost function y=1.80x+2.40(50−x)y = 1.80 x + 2.40 ( 50 - x )y=1.80x+2.40(50−x) .

What is the domain of the function f(x)=4+ln⁡(x−6)?\text { What is the domain of the function } f ( x ) = 4 + \ln ( x - 6 ) ? What is the domain of the function f(x)=4+ln(x−6)?

Evaluate (if possible) the function f(x)=−6x−5 at x=−2. Simplify the result. \text { Evaluate (if possible) the function } f ( x ) = - 6 x - 5 \text { at } x = - 2 \text {. Simplify the result. } Evaluate (if possible) the function f(x)=−6x−5 at x=−2. Simplify the result.

Students in a lab measured the breaking strength S (in pounds) of wood 2 inches thick, xxx inches high, and 12 inches long. The results are shown in the table below. Use a graphing utility to plot the data and graph the quadratic model. x 4 6 8 10 12 S 2370 4460 13,310 19,250 29,860

Find f−1(x) if f(x)=13−x2,0≤x≤13\text { Find } f ^ { - 1 } ( x ) \text { if } f ( x ) = \sqrt { 13 - x ^ { 2 } } , 0 \leq x \leq \sqrt { 13 } Find f−1(x) if f(x)=13−x2​,0≤x≤13​

Which of the following is the correct graph of y=2−x ? \text { Which of the following is the correct graph of } y = 2 - x \text { ? } Which of the following is the correct graph of y=2−x ?

Evaluate the function f(x)={2x+1,x<02x+2,x≥0 at f(5)\text { Evaluate the function } f ( x ) = \left\{ \begin{array} { l } 2 x + 1 , x < 0 \\2 x + 2 , x \geq 0\end{array} \text { at } f ( 5 ) \right. Evaluate the function f(x)={2x+1,x<02x+2,x≥0​ at f(5)

Sketch the graph of the equation: x=4−y2x = 4 - y ^ { 2 }x=4−y2

Sketch a graph of the equation y−8=2(x+4). \text { Sketch a graph of the equation } y - 8 = 2 ( x + 4 ) \text {. } Sketch a graph of the equation y−8=2(x+4).

Determine whether the function is even, odd, or neither. f(x)=x2(3−x)2f ( x ) = x ^ { 2 } ( 3 - x ) ^ { 2 }f(x)=x2(3−x)2

Evaluate the expression arccos (22) without using a calculator. \text { Evaluate the expression arccos } \left( \frac { \sqrt { 2 } } { 2 } \right) \text { without using a calculator. } Evaluate the expression arccos (22​​) without using a calculator.

moving conveyor is built to rise 1 meter for every 5 meters of horizontal change. Suppose the conveyor runs between two floors in a factory. Find the length of the conveyor if the Vertical distance between floors is 10 meters. Round your answer to the nearest meter.

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

all intercepts: $y = 64 x - x ^ { 3 }$

Use the Horizontal Line Test to determine whether the following statement is true or false. The function $f ( x ) = 14 ( x - 15 ) + 15$ is one-to-one on its entire domain and therefore has an inverse function.

Write the following expression as a logarithm of a single quantity. $\ln x - 4 \ln \left( x ^ { 2 } + 1 \right)$

You need 50 pounds of two commodities costing $1.80 and $2.40 per pound. Find the inverse function of the cost function $y = 1.80 x + 2.40 ( 50 - x )$ .

$\text { What is the domain of the function } f ( x ) = 4 + \ln ( x - 6 ) ?$

$\text { Evaluate (if possible) the function } f ( x ) = - 6 x - 5 \text { at } x = - 2 \text {. Simplify the result. }$

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 a graphing utility to plot the data and graph the quadratic model. x 4 6 8 10 12 S 2370 4460 13,310 19,250 29,860

$\text { Find } f ^ { - 1 } ( x ) \text { if } f ( x ) = \sqrt { 13 - x ^ { 2 } } , 0 \leq x \leq \sqrt { 13 }$

$\text { Which of the following is the correct graph of } y = 2 - x \text { ? }$

$\text { Evaluate the function } f ( x ) = \left\{ \begin{array} { l } 2 x + 1 , x < 0 \\2 x + 2 , x \geq 0\end{array} \text { at } f ( 5 ) \right.$

Sketch the graph of the equation: $x = 4 - y ^ { 2 }$

$\text { Sketch a graph of the equation } y - 8 = 2 ( x + 4 ) \text {. }$

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

$\text { Evaluate the expression arccos } \left( \frac { \sqrt { 2 } } { 2 } \right) \text { without using a calculator. }$