Question 1

Find the inverse of the function.
-$$f ( x ) = \sqrt { x - 8 } , x \geq 8$$

Accepted Answer

A)  $f ^ { - 1 } ( x ) = x ^ { 2 } + 8 , x \geq 0$ 
B)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \mathrm { x } ^ { 2 } - 8 , x \geq 0$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \mathrm { x } + 8 , \mathrm { x } \geq 0$ 
D)  Not a one-to-one function 
A)  $f ^ { - 1 } ( x ) = x ^ { 2 } + 8 , x \geq 0$ 
B)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \mathrm { x } ^ { 2 } - 8 , x \geq 0$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \mathrm { x } + 8 , \mathrm { x } \geq 0$ 
D)  Not a one-to-one function

Question 2

Provide an appropriate response.
-If $f ( x )$ is one-to-one, is $g ( x ) = f ( - x )$ also one-to-one? Explain.

Accepted Answer

A)  $g ( x )$ is a reflection of $f ( x )$ across the $y$-axis. It will be one-to-one. 
B)  There is not enough information to determine whether $g ( x )$ is one-to-one. 
C)  $g ( x )$ is a reflection of $f ( x )$ across the $x$-axis. It will be one-to-one. 
D)  $g ( x )$ is a reflection of $f ( x )$ across the line $y = x$. It will not be one-to-one. 
A)  $g ( x )$ is a reflection of $f ( x )$ across the $y$-axis. It will be one-to-one. 
B)  There is not enough information to determine whether $g ( x )$ is one-to-one. 
C)  $g ( x )$ is a reflection of $f ( x )$ across the $x$-axis. It will be one-to-one. 
D)  $g ( x )$ is a reflection of $f ( x )$ across the line $y = x$. It will not be one-to-one.

Question 3

Graph the function.
-$f(x)=2.5^{x}-2$

Accepted Answer

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

Question 4

Express the following logarithm as specified.
-$\ln \sqrt [ 3 ] { 4 }$ in terms of $\ln 2$

Accepted Answer

A)  $\frac { 1 } { 3 } \ln 4$ 
B)  $\frac { 3 } { 2 } \ln 2$ 
C)  $6 \ln 2$ 
D)  $\frac { 2 } { 3 } \ln 2$ 
A)  $\frac { 1 } { 3 } \ln 4$ 
B)  $\frac { 3 } { 2 } \ln 2$ 
C)  $6 \ln 2$ 
D)  $\frac { 2 } { 3 } \ln 2$

Question 5

Solve the problem.
-The amount of particulate matter left in solution during a filtering process decreases by the equation $$P = 900 ( 2 ) ^ { - 0.8 n }$$ where n is the number of filtering steps. Find the amounts left for n = 0 and n = 5. (Round to the nearest whole number.)

Accepted Answer

A)  1800, 56 
B)  900, 14,400 
C)  900, 28 
D)  900, 56 
A)  1800, 56 
B)  900, 14,400 
C)  900, 28 
D)  900, 56

Question 6

Find the inverse of the function.
-$$f ( x ) = \frac { 7 } { x + 7 }$$

Accepted Answer

A)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { - 7 \mathrm { x } + 7 } { \mathrm { x } }$ 
B)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 7 + 7 \mathrm { x } } { \mathrm { x } }$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } } { 7 + 7 \mathrm { x } }$ 
D)  Not a one-to-one function 
A)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { - 7 \mathrm { x } + 7 } { \mathrm { x } }$ 
B)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 7 + 7 \mathrm { x } } { \mathrm { x } }$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { \mathrm { x } } { 7 + 7 \mathrm { x } }$ 
D)  Not a one-to-one function

Question 7

Graph the function.
-$f ( x ) = 3 ( 3 x - 4 )$

Accepted Answer

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

Question 8

Graph the function.
-$f ( x ) = 2 ^ { - x }$

Accepted Answer

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

Question 9

Graph the function.
-$$f ( x ) = \left( \frac { 1 } { 3 } \right) ^ { x }$$

Accepted Answer

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

Question 10

Find the formula for the function.
-A point P in the first quadrant lies on the graph of the function f $f ( x ) = x ^ { 2 }$. Express the slope of the line joining P to the origin as a function of x.

Accepted Answer

A)  m = 2x 
B)  $m=\frac{2}{x}$ 
C)  m = x 
D)  $m=\frac{1}{x}$ 
A)  m = 2x 
B)  $m=\frac{2}{x}$ 
C)  m = x 
D)  $m=\frac{1}{x}$

Question 11

Use a graph to find an approximate solution to the equation. Round to the nearest thousandth.
-$$3 ^ { x } = 18$$

Accepted Answer

A)  0.380 
B)  6.000 
C)  2.631 
D)  1.792 
A)  0.380 
B)  6.000 
C)  2.631 
D)  1.792

Question 12

Solve the problem.
-The table shows the amount of yeast cells (measured as biomass) growing over a 7 -hour period in a nutrient. (a) Find a regression quadratic for the data. (b) Use the regression quadratic to predict the biomass of yeast in the nutrient after 10 hours.
$\begin{array}{l|cccccccc}
\text { Hour } & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \
\hline \text { Biomass } & 7.4 & 16.7 & 31.1 & 49.2 & 76.8 & 122.0 & 179.5 & 263.3
\end{array}$

Accepted Answer

A)  (a) $y = 5.4215 x ^ { 2 } - 7.1512 x + 15.768$
(b) $486.406$ 
B)  (a) $y = 5.7661 x ^ { 2 } - 8.1557 x + 13.284$
(b) $508.337$ 
C)  (a) $y = 4.5432 x ^ { 2 } + 6.8417 x + 19.925$
(b) $542.662$ 
D)  (a) $y = 5.9631 x ^ { 2 } - 7.1512 x + 13.925$
(b) $538.723$ 
A)  (a) $y = 5.4215 x ^ { 2 } - 7.1512 x + 15.768$
(b) $486.406$ 
B)  (a) $y = 5.7661 x ^ { 2 } - 8.1557 x + 13.284$
(b) $508.337$ 
C)  (a) $y = 4.5432 x ^ { 2 } + 6.8417 x + 19.925$
(b) $542.662$ 
D)  (a) $y = 5.9631 x ^ { 2 } - 7.1512 x + 13.925$
(b) $538.723$

Question 13

Consider the function y Can x be 0?
-$$\text { Graph the function } f ( x ) = \lceil x \rceil$$

Accepted Answer

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

Question 14

Provide an appropriate response.
-If $\mathrm { f } ( \mathrm { x } )$ is one-to-one, can anything be said about $h ( x ) = 6 f ( x ) + 3$ ? Is it also one-to-one? Give reasons for your answer.

Accepted Answer

A)  Yes, $h ( x )$ will be one-to-one. For every distinct value of $f ( x )$ there is one distinct value of $h ( x )$. 
B)  No, $h ( x )$ will not be one-to-one. The function $h ( x )$ assumes the same value for at least two different $f ( x )$-values. 
C)  Yes, $h ( x )$ will be one-to-one. The inverse of $f ( x )$ is $h ( x )$ and is therefore one-to-one. 
D)  No, $h ( x )$ will not be one-to-one. The function $h ( x )$ does not pass the horizontal line test. 
A)  Yes, $h ( x )$ will be one-to-one. For every distinct value of $f ( x )$ there is one distinct value of $h ( x )$. 
B)  No, $h ( x )$ will not be one-to-one. The function $h ( x )$ assumes the same value for at least two different $f ( x )$-values. 
C)  Yes, $h ( x )$ will be one-to-one. The inverse of $f ( x )$ is $h ( x )$ and is therefore one-to-one. 
D)  No, $h ( x )$ will not be one-to-one. The function $h ( x )$ does not pass the horizontal line test.

Question 15

Graph the function.
-$y=(5-x)^{3}-1$

Accepted Answer

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

Question 16

Simplify the expression.
-$$\log _ { 8 } 512$$

Accepted Answer

A)  8 
B)  24 
C)  512 
D)  3 
A)  8 
B)  24 
C)  512 
D)  3

Question 17

Find the domain and range of the inverse of the given function.
-$$f ( x ) = \frac { 8 } { x ^ { 2 } + 1 } , x \geq 0$$

Accepted Answer

A)  Domain: $( - \infty , 0 \}$; range: $[ - 8,0 )$ 
B)  Domain: $[ 0 , \infty )$; range: $( 0,8 ]$ 
C)  Domain: $( 0,8 ]$; range: $[ 0 , \infty )$ 
D)  Domain and range: $[ 0 , \infty )$ 
A)  Domain: $( - \infty , 0 \}$; range: $[ - 8,0 )$ 
B)  Domain: $[ 0 , \infty )$; range: $( 0,8 ]$ 
C)  Domain: $( 0,8 ]$; range: $[ 0 , \infty )$ 
D)  Domain and range: $[ 0 , \infty )$

Question 18

Graph the function.
-$y=\frac{1}{x}-4$

Accepted Answer

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

Question 19

One of sin x, cos x, and tan x is given. Find the other two if x lies in the specified interval.
-$$\sin x = \frac { 12 } { 13 } , \quad x \text { in } \left[ \frac { \pi } { 2 } , \pi \right]$$

Accepted Answer

A)  $\cos x = \frac { 5 } { 13 } , \tan x = \frac { 12 } { 5 }$ 
B)  $\cos x = - \frac { 5 } { 13 } , \tan x = - \frac { 5 } { 12 }$ 
C)  $\cos x = - \frac { 5 } { 13 } , \tan x = - \frac { 12 } { 5 }$ 
D)  $\cos x = \frac { 5 } { 13 } , \tan x = - \frac { 5 } { 12 }$ 
A)  $\cos x = \frac { 5 } { 13 } , \tan x = \frac { 12 } { 5 }$ 
B)  $\cos x = - \frac { 5 } { 13 } , \tan x = - \frac { 5 } { 12 }$ 
C)  $\cos x = - \frac { 5 } { 13 } , \tan x = - \frac { 12 } { 5 }$ 
D)  $\cos x = \frac { 5 } { 13 } , \tan x = - \frac { 5 } { 12 }$

Question 20

The problem tells by what factor and direction the graph of the given function is to be stretched or compressed. Give an
equation for the stretched or compressed graph.
-$y = x ^ { 2 } + 4 \quad$ compressed vertically by a factor of 2

Accepted Answer

A)  $y = \frac { x ^ { 2 } } { 2 } + 4$ 
B)  $y = 2 x ^ { 2 } + 8$ 
C)  $y = \frac { x ^ { 2 } } { 2 } + 2$ 
D)  $y = 4 x ^ { 2 } + 4$ 
A)  $y = \frac { x ^ { 2 } } { 2 } + 4$ 
B)  $y = 2 x ^ { 2 } + 8$ 
C)  $y = \frac { x ^ { 2 } } { 2 } + 2$ 
D)  $y = 4 x ^ { 2 } + 4$

Find the inverse of the function. - $f ( x ) = \sqrt { x - 8 } , x \geq 8$

Provide an appropriate response. -If $f ( x )$ is one-to-one, is $g ( x ) = f ( - x )$ also one-to-one? Explain.

Graph the function. - $f(x)=2.5^{x}-2$ $Graph the function. - f(x)=2.5^{x}-2$

Express the following logarithm as specified. - $\ln \sqrt [ 3 ] { 4 }$ in terms of $\ln 2$

Solve the problem. -The amount of particulate matter left in solution during a filtering process decreases by the equation $P = 900 ( 2 ) ^ { - 0.8 n }$ where n is the number of filtering steps. Find the amounts left for n = 0 and n = 5. (Round to the nearest whole number.)

Find the inverse of the function. - $f ( x ) = \frac { 7 } { x + 7 }$

Graph the function. - $f ( x ) = 3 ( 3 x - 4 )$

Graph the function. - $f ( x ) = 2 ^ { - x }$ $Graph the function. - f ( x ) = 2 ^ { - x }$

Graph the function. - $f ( x ) = \left( \frac { 1 } { 3 } \right) ^ { x }$ $Graph the function. - f ( x ) = \left( \frac { 1 } { 3 } \right) ^ { x }$

Find the formula for the function. -A point P in the first quadrant lies on the graph of the function f $f ( x ) = x ^ { 2 }$ . Express the slope of the line joining P to the origin as a function of x.

Use a graph to find an approximate solution to the equation. Round to the nearest thousandth. - $3 ^ { x } = 18$

Consider the function y Can x be 0? - $\text { Graph the function } f ( x ) = \lceil x \rceil$ $Consider the function y Can x be 0? - \text { Graph the function } f ( x ) = \lceil x \rceil$

Provide an appropriate response. -If $\mathrm { f } ( \mathrm { x } )$ is one-to-one, can anything be said about $h ( x ) = 6 f ( x ) + 3$ ? Is it also one-to-one? Give reasons for your answer.

Graph the function. - $y=(5-x)^{3}-1$ $Graph the function. - y=(5-x)^{3}-1$

Simplify the expression. - $\log _ { 8 } 512$

Find the domain and range of the inverse of the given function. - $f ( x ) = \frac { 8 } { x ^ { 2 } + 1 } , x \geq 0$

Graph the function. - $y=\frac{1}{x}-4$ $Graph the function. - y=\frac{1}{x}-4$

One of sin x, cos x, and tan x is given. Find the other two if x lies in the specified interval. - $\sin x = \frac { 12 } { 13 } , \quad x \text { in } \left[ \frac { \pi } { 2 } , \pi \right]$

The problem tells by what factor and direction the graph of the given function is to be stretched or compressed. Give an equation for the stretched or compressed graph. - $y = x ^ { 2 } + 4 \quad$ compressed vertically by a factor of 2

Limits and Continuity

Derivatives

Applications of Derivatives

Integrals

Applications of Definite Integrals

Integrals and Transcendental Functions

Techniques of Integration

First-Order Differential Equations

Infinite Sequences and Series

Parametric Equations and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions and Motion in Space

Partial Derivatives

Multiple Integrals

Integrals and Vector Fields

Filters

Exam 2: Functions

Find the inverse of the function. - f(x)=x−8,x≥8f ( x ) = \sqrt { x - 8 } , x \geq 8f(x)=x−8​,x≥8

Provide an appropriate response. -If f(x)f ( x )f(x) is one-to-one, is g(x)=f(−x)g ( x ) = f ( - x )g(x)=f(−x) also one-to-one? Explain.

Graph the function. - f(x)=2.5x−2f(x)=2.5^{x}-2f(x)=2.5x−2

Express the following logarithm as specified. - ln⁡43\ln \sqrt [ 3 ] { 4 }ln34​ in terms of ln⁡2\ln 2ln2

Find the inverse of the function. - f(x)=7x+7f ( x ) = \frac { 7 } { x + 7 }f(x)=x+77​

Graph the function. - f(x)=3(3x−4)f ( x ) = 3 ( 3 x - 4 )f(x)=3(3x−4)

Graph the function. - f(x)=2−xf ( x ) = 2 ^ { - x }f(x)=2−x

Graph the function. - f(x)=(13)xf ( x ) = \left( \frac { 1 } { 3 } \right) ^ { x }f(x)=(31​)x

Find the formula for the function. -A point P in the first quadrant lies on the graph of the function f f(x)=x2f ( x ) = x ^ { 2 }f(x)=x2 . Express the slope of the line joining P to the origin as a function of x.

Use a graph to find an approximate solution to the equation. Round to the nearest thousandth. - 3x=183 ^ { x } = 183x=18

Consider the function y Can x be 0? - Graph the function f(x)=⌈x⌉\text { Graph the function } f ( x ) = \lceil x \rceil Graph the function f(x)=⌈x⌉

Provide an appropriate response. -If f(x)\mathrm { f } ( \mathrm { x } )f(x) is one-to-one, can anything be said about h(x)=6f(x)+3h ( x ) = 6 f ( x ) + 3h(x)=6f(x)+3 ? Is it also one-to-one? Give reasons for your answer.

Graph the function. - y=(5−x)3−1y=(5-x)^{3}-1y=(5−x)3−1

Simplify the expression. - log⁡8512\log _ { 8 } 512log8​512

Find the domain and range of the inverse of the given function. - f(x)=8x2+1,x≥0f ( x ) = \frac { 8 } { x ^ { 2 } + 1 } , x \geq 0f(x)=x2+18​,x≥0

Graph the function. - y=1x−4y=\frac{1}{x}-4y=x1​−4

One of sin x, cos x, and tan x is given. Find the other two if x lies in the specified interval. - sin⁡x=1213,x in [π2,π]\sin x = \frac { 12 } { 13 } , \quad x \text { in } \left[ \frac { \pi } { 2 } , \pi \right]sinx=1312​,x in [2π​,π]

The problem tells by what factor and direction the graph of the given function is to be stretched or compressed. Give an equation for the stretched or compressed graph. - y=x2+4y = x ^ { 2 } + 4 \quady=x2+4 compressed vertically by a factor of 2

Limits and Continuity

Derivatives

Applications of Derivatives

Integrals

Applications of Definite Integrals

Integrals and Transcendental Functions

Techniques of Integration

First-Order Differential Equations

Infinite Sequences and Series

Parametric Equations and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions and Motion in Space

Partial Derivatives

Multiple Integrals

Integrals and Vector Fields

Filters

Find the inverse of the function. - $f ( x ) = \sqrt { x - 8 } , x \geq 8$

Provide an appropriate response. -If $f ( x )$ is one-to-one, is $g ( x ) = f ( - x )$ also one-to-one? Explain.

Graph the function. - $f(x)=2.5^{x}-2$ $Graph the function. - f(x)=2.5^{x}-2$

Express the following logarithm as specified. - $\ln \sqrt [ 3 ] { 4 }$ in terms of $\ln 2$

Find the inverse of the function. - $f ( x ) = \frac { 7 } { x + 7 }$

Graph the function. - $f ( x ) = 3 ( 3 x - 4 )$

Graph the function. - $f ( x ) = 2 ^ { - x }$ $Graph the function. - f ( x ) = 2 ^ { - x }$

Graph the function. - $f ( x ) = \left( \frac { 1 } { 3 } \right) ^ { x }$ $Graph the function. - f ( x ) = \left( \frac { 1 } { 3 } \right) ^ { x }$

Find the formula for the function. -A point P in the first quadrant lies on the graph of the function f $f ( x ) = x ^ { 2 }$ . Express the slope of the line joining P to the origin as a function of x.

Use a graph to find an approximate solution to the equation. Round to the nearest thousandth. - $3 ^ { x } = 18$

Consider the function y Can x be 0? - $\text { Graph the function } f ( x ) = \lceil x \rceil$ $Consider the function y Can x be 0? - \text { Graph the function } f ( x ) = \lceil x \rceil$

Provide an appropriate response. -If $\mathrm { f } ( \mathrm { x } )$ is one-to-one, can anything be said about $h ( x ) = 6 f ( x ) + 3$ ? Is it also one-to-one? Give reasons for your answer.

Graph the function. - $y=(5-x)^{3}-1$ $Graph the function. - y=(5-x)^{3}-1$

Simplify the expression. - $\log _ { 8 } 512$

Find the domain and range of the inverse of the given function. - $f ( x ) = \frac { 8 } { x ^ { 2 } + 1 } , x \geq 0$

Graph the function. - $y=\frac{1}{x}-4$ $Graph the function. - y=\frac{1}{x}-4$

One of sin x, cos x, and tan x is given. Find the other two if x lies in the specified interval. - $\sin x = \frac { 12 } { 13 } , \quad x \text { in } \left[ \frac { \pi } { 2 } , \pi \right]$

The problem tells by what factor and direction the graph of the given function is to be stretched or compressed. Give an equation for the stretched or compressed graph. - $y = x ^ { 2 } + 4 \quad$ compressed vertically by a factor of 2