Question 1

Find the domain. $g ( t ) = \frac { 1 } { t ^ { 2 } - 7 t + 12 }$

Accepted Answer

A)  $( - \infty , - 4 ) \cup ( - 4,3 ) \cup ( 3 , \infty )$ 
B)  $( - \infty , 3 ) \cup ( 3,4 ) \cup ( 4 , \infty )$ 
C)  $( - \infty , - 4 ) \cup ( 3 , \infty )$ 
D)  $( - \infty , 4 ) \cup ( 5 , \infty )$ 
E)  $( - \infty , - 3 ) \cup ( 3 , \infty )$ 
A)  $( - \infty , - 4 ) \cup ( - 4,3 ) \cup ( 3 , \infty )$ 
B)  $( - \infty , 3 ) \cup ( 3,4 ) \cup ( 4 , \infty )$ 
C)  $( - \infty , - 4 ) \cup ( 3 , \infty )$ 
D)  $( - \infty , 4 ) \cup ( 5 , \infty )$ 
E)  $( - \infty , - 3 ) \cup ( 3 , \infty )$ B

Question 2

Let f (x) = x 2 . Find and simplify the indicated difference quotient. $\frac { f ( y + h ) - f ( y ) } { h }$

Accepted Answer

A)  y 2  - h 
B)  2y - h 
C)  2y + h 2  
D)  2y + h 
E)  y + h 
A)  y 2  - h 
B)  2y - h 
C)  2y + h 2  
D)  2y + h 
E)  y + h D

Question 3

Using the results in the table, graph the functions y = x 2 , y = x 2  - 2, and y = x 2  + 2 on the same set of axes. x
X 2 
X 2  - 2
X 2  + 2
0
0
-2
2 $\pm$ 1
1
-1
3 $\pm$ 2
4
2
6 $\pm$ 3
9
7
11

Accepted Answer

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

Question 4

Specify the domain and range of the given function. (The axes are marked in one-unit intervals.)

Accepted Answer

A)  domain: $[ - 2,4 )$ ; range: $[ - 3,3 ]$ 
B)  domain: $[ - 3,1 ) \cup ( 1,3 ]$ ; range: $[ - 2,4 ]$ 
C)  domain: $[ - 3,3 ]$ ; range: $[ - 2,4 )$ 
D)  domain: $[ - 3,3 ]$ ; range: $[ - 2 , - 1 )$ 
E)  domain: $[ - 3,1 ) \cup ( 1,3 ]$ ; range: $[ - 2,4 )$ 
A)  domain: $[ - 2,4 )$ ; range: $[ - 3,3 ]$ 
B)  domain: $[ - 3,1 ) \cup ( 1,3 ]$ ; range: $[ - 2,4 ]$ 
C)  domain: $[ - 3,3 ]$ ; range: $[ - 2,4 )$ 
D)  domain: $[ - 3,3 ]$ ; range: $[ - 2 , - 1 )$ 
E)  domain: $[ - 3,1 ) \cup ( 1,3 ]$ ; range: $[ - 2,4 )$

Question 5

Assume that the accompanying viewing rectangle shows the essential features of the graph of f(x) = -x 3 + 4x+ 2. Use a graphing utility to estimate to the nearest hundredth the coordinates of the turning points.   f(x) = -x 3 + 4x+ 2 [- 4, 4, 2] by [- 12, 12, 6]

Accepted Answer

A)  (- 1.14, - 1.08),(1.14, 5.08) 
B)  (- 1.14, - 1.09),(1.14, 5.09) 
C)  (- 1.15, - 1.07),(1.15, 5.07) 
D)  (- 1.15, - 1.08),(1.15, 5.08) 
E)  (- 1.16, - 1.08),(1.16, 5.08) 
A)  (- 1.14, - 1.08),(1.14, 5.08) 
B)  (- 1.14, - 1.09),(1.14, 5.09) 
C)  (- 1.15, - 1.07),(1.15, 5.07) 
D)  (- 1.15, - 1.08),(1.15, 5.08) 
E)  (- 1.16, - 1.08),(1.16, 5.08)

Question 6

Suppose that in a certain biology lab experiment, the number of bacteria is related to the temperature T of the environment by the function $N ( T ) = - 2 T ^ { 2 } + 240 T - 5,100 ( 40 \leq t \leq 90 )$ Here, N(T) represents the number of bacteria present when the temperature is T degrees Fahrenheit. Also, suppose that t hr after the experiment begins, the temperature is given by $T ( t ) = 10 t + 40 ( 0 \leq t \leq 5 )$ How many bacteria are present when t = 5 hr?

Accepted Answer

A)  300 
B)  900 
C)  1,200 
D)  400 
E)  600 
A)  300 
B)  900 
C)  1,200 
D)  400 
E)  600

Question 7

Assume that the domain of $f$ and $f ^ { - 1 }$ is $( - \infty , \infty )$ . Solve for t. $$f \left( \frac { 6 - 2 t } { 6 + 2 t } \right) = 12 ; f ^ { - 1 } ( 12 ) = - 3$$ .

Accepted Answer

A)  t = - 6 
B)  t = 12 
C)  t = 7 
D)  t = - 7 
E)  t = -7 
A)  t = - 6 
B)  t = 12 
C)  t = 7 
D)  t = - 7 
E)  t = -7

Question 8

Find the domain. $g ( t ) = \sqrt [ 3 ] { t ^ { 2 } - 9 t + 20 }$

Accepted Answer

A)  $( - \infty , \infty )$ 
B)  $( - \infty , 4 ) \cup ( 5 , \infty )$ 
C)  $[ 4,5 ]$ 
D)  $( - \infty , 4 ) \cup ( 4,5 ) \cup ( 5 , \infty )$ 
E)  $[ - 4 , \infty )$ 
A)  $( - \infty , \infty )$ 
B)  $( - \infty , 4 ) \cup ( 5 , \infty )$ 
C)  $[ 4,5 ]$ 
D)  $( - \infty , 4 ) \cup ( 4,5 ) \cup ( 5 , \infty )$ 
E)  $[ - 4 , \infty )$

Question 9

Find the domain. $H ( t ) = \sqrt [ 3 ] { \frac { 5 t - 4 } { 7 - 2 t } }$

Accepted Answer

A)  $\left( - \infty , \frac { 4 } { 5 } \right) \cup \left( \frac { 4 } { 5 } , \frac { 7 } { 2 } \right) \cup \left( \frac { 7 } { 2 } , \infty \right)$ 
B)  $\left( - \infty , \frac { 4 } { 5 } \right] \cup \left( \frac { 7 } { 2 } , \infty \right)$ 
C)  $\left( \frac { 4 } { 5 } , \frac { 7 } { 2 } \right)$ 
D)  $\left( - \infty , \frac { 7 } { 2 } \right) \cup \left( \frac { 7 } { 2 } , \infty \right)$ 
E)  $\left( - \infty , \frac { 4 } { 5 } \right) \cup \left( \frac { 7 } { 2 } , \infty \right)$ 
A)  $\left( - \infty , \frac { 4 } { 5 } \right) \cup \left( \frac { 4 } { 5 } , \frac { 7 } { 2 } \right) \cup \left( \frac { 7 } { 2 } , \infty \right)$ 
B)  $\left( - \infty , \frac { 4 } { 5 } \right] \cup \left( \frac { 7 } { 2 } , \infty \right)$ 
C)  $\left( \frac { 4 } { 5 } , \frac { 7 } { 2 } \right)$ 
D)  $\left( - \infty , \frac { 7 } { 2 } \right) \cup \left( \frac { 7 } { 2 } , \infty \right)$ 
E)  $\left( - \infty , \frac { 4 } { 5 } \right) \cup \left( \frac { 7 } { 2 } , \infty \right)$

Question 10

Let T (x) = 4x 2  - 3x. Find (and simplify) the expression. T (x + h) - T (x - h)

Accepted Answer

A)  16h - 3x 
B)  16hx - 6h 
C)  8x + 4h 
D)  8x - 3h 
E)  16hx + 3h 
A)  16h - 3x 
B)  16hx - 6h 
C)  8x + 4h 
D)  8x - 3h 
E)  16hx + 3h

Question 11

Set up a table and graph the function $y = 1 / x .$

Accepted Answer

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

Question 12

Sketch the graph. $$y = \left\{ \begin{array} { l l } 
2 \sqrt { 1 - x ^ { 2 } } & \text { if } - 1 \leq x < 1 \
\frac { 2 } { x } & \text { if } x \geq 1
\end{array} \right.$$

Accepted Answer

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

Question 13

Given that f and g are inverse functions. If f(7) = 12, what is g(12)?

Accepted Answer

A)  17 
B)  12 
C)  5 
D)  4 
E)  7 
A)  17 
B)  12 
C)  5 
D)  4 
E)  7

Question 14

Use a graphing utility to graph the function and then apply the horizontal line test to see whether the function is one-to-one. y = x 7  + 5x
A) True
B) False

Accepted Answer

A) True 
 B)False

Question 15

Find the domain. $h ( x ) = \sqrt { x ^ { 2 } - 49 }$

Accepted Answer

A)  $( 7 , \infty )$ 
B)  $( - \infty , 49 ] \cup [ 49 , \infty )$ 
C)  $( - \infty , - 7 ) \cup ( 7 , \infty )$ 
D)  $( - \infty , - 7 ] \cup [ 7 , \infty )$ 
E)  $( - 7,7 )$ 
A)  $( 7 , \infty )$ 
B)  $( - \infty , 49 ] \cup [ 49 , \infty )$ 
C)  $( - \infty , - 7 ) \cup ( 7 , \infty )$ 
D)  $( - \infty , - 7 ] \cup [ 7 , \infty )$ 
E)  $( - 7,7 )$

Question 16

Determine the domain and the range. $F ( x ) = \frac { x ^ { 3 } + 6 } { x ^ { 3 } - 2 }$

Accepted Answer

A)  domain: $( - \infty , \sqrt [ 3 ] { 2 } ) \cup ( \sqrt [ 3 ] { 2 } , \infty )$ ; range: $( - \infty , \infty )$ 
B)  domain: $( - \infty , \sqrt [ 3 ] { 2 } ) \cup ( \sqrt [ 3 ] { 2 } , \infty )$ ; range: $( - \infty , 1 ) \cup ( 1 , \infty )$ 
C)  domain: $\left( - \infty , 2 ^ { 3 } \right) \cup \left( 2 ^ { 3 } , \infty \right)$ ; range: $( - \infty , 1 ) \cup ( 1 , \infty )$ 
D)  domain: $( - \infty , - \sqrt [ 3 ] { 2 } ) \cup ( - \sqrt [ 3 ] { 2 } , \infty )$ ; range: $( - \infty , \infty )$ 
E)  domain: $( - \infty , \sqrt [ 3 ] { 2 } ) \cup ( \sqrt [ 3 ] { 2 } , \infty )$ ; range: $( - \infty , 0 ) \cup ( 0 , \infty )$ 
A)  domain: $( - \infty , \sqrt [ 3 ] { 2 } ) \cup ( \sqrt [ 3 ] { 2 } , \infty )$ ; range: $( - \infty , \infty )$ 
B)  domain: $( - \infty , \sqrt [ 3 ] { 2 } ) \cup ( \sqrt [ 3 ] { 2 } , \infty )$ ; range: $( - \infty , 1 ) \cup ( 1 , \infty )$ 
C)  domain: $\left( - \infty , 2 ^ { 3 } \right) \cup \left( 2 ^ { 3 } , \infty \right)$ ; range: $( - \infty , 1 ) \cup ( 1 , \infty )$ 
D)  domain: $( - \infty , - \sqrt [ 3 ] { 2 } ) \cup ( - \sqrt [ 3 ] { 2 } , \infty )$ ; range: $( - \infty , \infty )$ 
E)  domain: $( - \infty , \sqrt [ 3 ] { 2 } ) \cup ( \sqrt [ 3 ] { 2 } , \infty )$ ; range: $( - \infty , 0 ) \cup ( 0 , \infty )$

Question 17

A spherical weather balloon is being inflated in such a way that the radius is given by $r = g ( t ) = \frac { 1 } { 2 } t + 2$ Assume that r is in meters and t is in seconds, with t = 0 corresponding to the time that inflation begins. If the volume of a sphere of radius r is given by $V ( r ) = \frac { 4 } { 3 } \pi r ^ { 3 }$ find the time at which the volume of the balloon is $36 \pi \mathrm { m } ^ { 3 }$

Accepted Answer

A)  t = 5 sec 
B)  t = 6 sec 
C)  t = 3 sec 
D)  t = 2 sec 
E)  t = 1 sec 
A)  t = 5 sec 
B)  t = 6 sec 
C)  t = 3 sec 
D)  t = 2 sec 
E)  t = 1 sec

Question 18

Let $g ( t ) = \frac { 4 } { t } + 6$ . Find g - 1 (t).

Accepted Answer

A)  $g ^ { - 1 } ( t ) = \frac { 4 } { t - 6 }$ 
B)  $g ^ { - 1 } ( t ) = \frac { 4 } { t } + 6$ 
C)  $g ^ { - 1 } ( t ) = \frac { t } { 4 } - 6$ 
D)  $g ^ { - 1 } ( t ) = \frac { 7 } { t } - 6$ 
E)  $g ^ { - 1 } ( t ) = \frac { 6 } { t - 4 }$ 
A)  $g ^ { - 1 } ( t ) = \frac { 4 } { t - 6 }$ 
B)  $g ^ { - 1 } ( t ) = \frac { 4 } { t } + 6$ 
C)  $g ^ { - 1 } ( t ) = \frac { t } { 4 } - 6$ 
D)  $g ^ { - 1 } ( t ) = \frac { 7 } { t } - 6$ 
E)  $g ^ { - 1 } ( t ) = \frac { 6 } { t - 4 }$

Question 19

Set up a table and graph the function $y = x ^ { 2 } - 2$ .

Accepted Answer

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

Question 20

Find the domain. $g ( t ) = \sqrt { t ^ { 2 } - 5 t + 6 }$

Accepted Answer

A)  $( - \infty , - 3 ] \cup [ 2 , \infty )$ 
B)  $( - \infty , 2 ) \cup ( 2,3 ) \cup ( 3 , \infty )$ 
C)  $[ 2,3 ]$ 
D)  $( - \infty , 2 ] \cup [ 3 , \infty )$ 
E)  $( - \infty , 2 ) \cup ( 3 , \infty )$ 
A)  $( - \infty , - 3 ] \cup [ 2 , \infty )$ 
B)  $( - \infty , 2 ) \cup ( 2,3 ) \cup ( 3 , \infty )$ 
C)  $[ 2,3 ]$ 
D)  $( - \infty , 2 ] \cup [ 3 , \infty )$ 
E)  $( - \infty , 2 ) \cup ( 3 , \infty )$

Find the domain. $g ( t ) = \frac { 1 } { t ^ { 2 } - 7 t + 12 }$

Let f (x) = x². Find and simplify the indicated difference quotient. $\frac { f ( y + h ) - f ( y ) } { h }$

Specify the domain and range of the given function. (The axes are marked in one-unit intervals.)

Assume that the accompanying viewing rectangle shows the essential features of the graph of f(x) = -x³+ 4x+ 2. Use a graphing utility to estimate to the nearest hundredth the coordinates of the turning points. f(x) = -x³+ 4x+ 2 [- 4, 4, 2] by [- 12, 12, 6]

Assume that the domain of $f$ and $f ^ { - 1 }$ is $( - \infty , \infty )$ . Solve for t. $f \left( \frac { 6 - 2 t } { 6 + 2 t } \right) = 12 ; f ^ { - 1 } ( 12 ) = - 3$ .

Find the domain. $g ( t ) = \sqrt [ 3 ] { t ^ { 2 } - 9 t + 20 }$

Find the domain. $H ( t ) = \sqrt [ 3 ] { \frac { 5 t - 4 } { 7 - 2 t } }$

Let T (x) = 4x² - 3x. Find (and simplify) the expression. T (x + h) - T (x - h)

Set up a table and graph the function $y = 1 / x .$

Sketch the graph. $y = \left\{ \begin{array} { l l } 2 \sqrt { 1 - x ^ { 2 } } & \text { if } - 1 \leq x < 1 \\\frac { 2 } { x } & \text { if } x \geq 1\end{array} \right.$

Given that f and g are inverse functions. If f(7) = 12, what is g(12)?

Use a graphing utility to graph the function and then apply the horizontal line test to see whether the function is one-to-one. y = x⁷ + 5x A) True B) False

Find the domain. $h ( x ) = \sqrt { x ^ { 2 } - 49 }$

Determine the domain and the range. $F ( x ) = \frac { x ^ { 3 } + 6 } { x ^ { 3 } - 2 }$

Let $g ( t ) = \frac { 4 } { t } + 6$ . Find g^{- 1}(t).

Set up a table and graph the function $y = x ^ { 2 } - 2$ .

Find the domain. $g ( t ) = \sqrt { t ^ { 2 } - 5 t + 6 }$

Fundamentals

Equations and Inequalities

Polynomial and Rational Functions Applications to Optimization

Exponential and Logarithmic Functions

An Introduction to Trigonometry Via Right Triangles

The Trigonometric Functions

Graphs of the Trigonometric Functions

Analytical Trigonometry

Additional Topics in Trigonometry

Systems of Equations

The Conic Sections

Roots of Polynomial Equations

Additional Topics in Algebra

Filters

Exam 3: Functions

Find the domain. g(t)=1t2−7t+12g ( t ) = \frac { 1 } { t ^ { 2 } - 7 t + 12 }g(t)=t2−7t+121​

Let f (x) = x 2 . Find and simplify the indicated difference quotient. f(y+h)−f(y)h\frac { f ( y + h ) - f ( y ) } { h }hf(y+h)−f(y)​

Using the results in the table, graph the functions y = x 2 , y = x 2 - 2, and y = x 2 + 2 on the same set of axes. x X 2 X 2 - 2 X 2 + 2 0 0 -2 2 ±\pm± 1 1 -1 3 ±\pm± 2 4 2 6 ±\pm± 3 9 7 11

Specify the domain and range of the given function. (The axes are marked in one-unit intervals.)

Assume that the accompanying viewing rectangle shows the essential features of the graph of f(x) = -x 3 + 4x+ 2. Use a graphing utility to estimate to the nearest hundredth the coordinates of the turning points. f(x) = -x 3 + 4x+ 2 [- 4, 4, 2] by [- 12, 12, 6]

Assume that the domain of fff and f−1f ^ { - 1 }f−1 is (−∞,∞)( - \infty , \infty )(−∞,∞) . Solve for t. f(6−2t6+2t)=12;f−1(12)=−3f \left( \frac { 6 - 2 t } { 6 + 2 t } \right) = 12 ; f ^ { - 1 } ( 12 ) = - 3f(6+2t6−2t​)=12;f−1(12)=−3 .

Find the domain. g(t)=t2−9t+203g ( t ) = \sqrt [ 3 ] { t ^ { 2 } - 9 t + 20 }g(t)=3t2−9t+20​

Find the domain. H(t)=5t−47−2t3H ( t ) = \sqrt [ 3 ] { \frac { 5 t - 4 } { 7 - 2 t } }H(t)=37−2t5t−4​​

Let T (x) = 4x 2 - 3x. Find (and simplify) the expression. T (x + h) - T (x - h)

Set up a table and graph the function y=1/x.y = 1 / x .y=1/x.

Sketch the graph. y={21−x2 if −1≤x<12x if x≥1y = \left\{ \begin{array} { l l } 2 \sqrt { 1 - x ^ { 2 } } & \text { if } - 1 \leq x < 1 \\\frac { 2 } { x } & \text { if } x \geq 1\end{array} \right.y={21−x2​x2​​ if −1≤x<1 if x≥1​

Given that f and g are inverse functions. If f(7) = 12, what is g(12)?

Use a graphing utility to graph the function and then apply the horizontal line test to see whether the function is one-to-one. y = x 7 + 5x A) True B) False

Find the domain. h(x)=x2−49h ( x ) = \sqrt { x ^ { 2 } - 49 }h(x)=x2−49​

Determine the domain and the range. F(x)=x3+6x3−2F ( x ) = \frac { x ^ { 3 } + 6 } { x ^ { 3 } - 2 }F(x)=x3−2x3+6​

Let g(t)=4t+6g ( t ) = \frac { 4 } { t } + 6g(t)=t4​+6 . Find g - 1 (t).

Set up a table and graph the function y=x2−2y = x ^ { 2 } - 2y=x2−2 .

Find the domain. g(t)=t2−5t+6g ( t ) = \sqrt { t ^ { 2 } - 5 t + 6 }g(t)=t2−5t+6​

Fundamentals

Equations and Inequalities

Polynomial and Rational Functions Applications to Optimization

Exponential and Logarithmic Functions

An Introduction to Trigonometry Via Right Triangles

The Trigonometric Functions

Graphs of the Trigonometric Functions

Analytical Trigonometry

Additional Topics in Trigonometry

Systems of Equations

The Conic Sections

Roots of Polynomial Equations

Additional Topics in Algebra

Filters

Find the domain. $g ( t ) = \frac { 1 } { t ^ { 2 } - 7 t + 12 }$

Let f (x) = x². Find and simplify the indicated difference quotient. $\frac { f ( y + h ) - f ( y ) } { h }$

Assume that the accompanying viewing rectangle shows the essential features of the graph of f(x) = -x³+ 4x+ 2. Use a graphing utility to estimate to the nearest hundredth the coordinates of the turning points. f(x) = -x³+ 4x+ 2 [- 4, 4, 2] by [- 12, 12, 6]

Assume that the domain of $f$ and $f ^ { - 1 }$ is $( - \infty , \infty )$ . Solve for t. $f \left( \frac { 6 - 2 t } { 6 + 2 t } \right) = 12 ; f ^ { - 1 } ( 12 ) = - 3$ .

Find the domain. $g ( t ) = \sqrt [ 3 ] { t ^ { 2 } - 9 t + 20 }$

Find the domain. $H ( t ) = \sqrt [ 3 ] { \frac { 5 t - 4 } { 7 - 2 t } }$

Let T (x) = 4x² - 3x. Find (and simplify) the expression. T (x + h) - T (x - h)

Set up a table and graph the function $y = 1 / x .$

Sketch the graph. $y = \left\{ \begin{array} { l l } 2 \sqrt { 1 - x ^ { 2 } } & \text { if } - 1 \leq x < 1 \\\frac { 2 } { x } & \text { if } x \geq 1\end{array} \right.$

Use a graphing utility to graph the function and then apply the horizontal line test to see whether the function is one-to-one. y = x⁷ + 5x A) True B) False

Find the domain. $h ( x ) = \sqrt { x ^ { 2 } - 49 }$

Determine the domain and the range. $F ( x ) = \frac { x ^ { 3 } + 6 } { x ^ { 3 } - 2 }$

Let $g ( t ) = \frac { 4 } { t } + 6$ . Find g^{- 1}(t).

Set up a table and graph the function $y = x ^ { 2 } - 2$ .

Find the domain. $g ( t ) = \sqrt { t ^ { 2 } - 5 t + 6 }$