Question 1

Determine if the function is even, odd, or neither.
-$$f ( x ) = - 8 x ^ { 5 } + 3 x ^ { 3 }$$

Accepted Answer

A)  Even 
B)  Odd 
C)  Neither 
A)  Even 
B)  Odd 
C)  Neither

Question 2

Use the laws of exponents to simplify. Do not use negative exponents in your answer.
-$\frac { 2 ^ { - 7 } } { 2 ^ { 3 } }$

Accepted Answer

A)  $\frac { 1 } { 2 ^ { 10 } }$ 
B)  $\frac { 1 } { 2 ^ { 4 } }$ 
C)  $2 ^ { 4 }$ 
D)  $2 ^ { 10 }$ 
A)  $\frac { 1 } { 2 ^ { 10 } }$ 
B)  $\frac { 1 } { 2 ^ { 4 } }$ 
C)  $2 ^ { 4 }$ 
D)  $2 ^ { 10 }$

Question 3

Solve for the angle , where 0 2
-$\sin 2 \theta + \cos \theta = 0$

Accepted Answer

A)  $\theta = \frac { \pi } { 6 } , \frac { 5 \pi } { 6 } , \frac { 7 \pi } { 6 } , \frac { 11 \pi } { 6 }$ 
B)  $\theta = \frac { \pi } { 2 } , \frac { 3 \pi } { 2 } , \frac { 7 \pi } { 6 } , \frac { 11 \pi } { 6 }$ 
C)  $\theta = \frac { \pi } { 2 } , \frac { 3 \pi } { 2 } , \frac { \pi } { 6 } , \frac { 5 \pi } { 6 }$ 
D)  $\frac { 3 \pi } { 4 } , \frac { 5 \pi } { 4 } , \frac { 7 \pi } { 6 } , \frac { 11 \pi } { 6 }$ 
A)  $\theta = \frac { \pi } { 6 } , \frac { 5 \pi } { 6 } , \frac { 7 \pi } { 6 } , \frac { 11 \pi } { 6 }$ 
B)  $\theta = \frac { \pi } { 2 } , \frac { 3 \pi } { 2 } , \frac { 7 \pi } { 6 } , \frac { 11 \pi } { 6 }$ 
C)  $\theta = \frac { \pi } { 2 } , \frac { 3 \pi } { 2 } , \frac { \pi } { 6 } , \frac { 5 \pi } { 6 }$ 
D)  $\frac { 3 \pi } { 4 } , \frac { 5 \pi } { 4 } , \frac { 7 \pi } { 6 } , \frac { 11 \pi } { 6 }$

Question 4

Use a graphing calculator or computer to determine which of the given viewing windows displays the most appropriate
graph of the specified function.
-$$f ( x ) = \frac { x ^ { 2 } - 1 } { x ^ { 2 } + 1 }$$

Accepted Answer

A)  $[ - 10,10 ]$ by $[ - 2,2 ]$ 
B)  $[ - 5,5 ]$ by $[ - 15,15 ]$ 
C)  $[ - 10,10 ]$ by $[ - 10,10 ]$ 
D)  $[ - 1,1 ]$ by $[ - 2,2 ]$ 
A)  $[ - 10,10 ]$ by $[ - 2,2 ]$ 
B)  $[ - 5,5 ]$ by $[ - 15,15 ]$ 
C)  $[ - 10,10 ]$ by $[ - 10,10 ]$ 
D)  $[ - 1,1 ]$ by $[ - 2,2 ]$

Question 5

Find the exact function value.
-$\sin ^ { - 1 } ( 0 )$

Accepted Answer

A)  $\frac { \pi } { 2 }$ 
B)  0 
C)  $\pi$ 
D)  $- \frac { \pi } { 2 }$ 
A)  $\frac { \pi } { 2 }$ 
B)  0 
C)  $\pi$ 
D)  $- \frac { \pi } { 2 }$

Question 6

State the period of the function and graph.
-$\cos \left(x-\frac{\pi}{4}\right)+3$

Accepted Answer

A)  Period $2 \pi$
  
B)   Period $2 \pi$
  
C)  $\text { Period } 2 \pi$
  
D)  $\text { Period } 2 \pi$
  
A)  Period $2 \pi$
  
B)   Period $2 \pi$
  
C)  $\text { Period } 2 \pi$
  
D)  $\text { Period } 2 \pi$

Question 7

Determine if the function is even, odd, or neither.
-$$f ( x ) = ( x + 5 ) ( x + 8 )$$

Accepted Answer

A)  Even 
B)  Odd 
C)  Neither 
A)  Even 
B)  Odd 
C)  Neither

Question 8

Find the inverse of the function.
-$$f ( x ) = \sqrt { x + 9 }$$

Accepted Answer

A)  $f ^ { - 1 } ( x ) = \sqrt { x - 9 }$ 
B)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \mathrm { x } ^ { 2 } - 9 , x \geq 0$ 
C)  Not a one-to-one function 
D)  $f ^ { - 1 } ( x ) = ( x + 9 ) ^ { 2 }$ 
A)  $f ^ { - 1 } ( x ) = \sqrt { x - 9 }$ 
B)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \mathrm { x } ^ { 2 } - 9 , x \geq 0$ 
C)  Not a one-to-one function 
D)  $f ^ { - 1 } ( x ) = ( x + 9 ) ^ { 2 }$

Question 9

Is the function graphed below one-to-one?
-

Accepted Answer

A) True 
 B)False

Question 10

Solve the problem.
-In the formula N $$\mathrm { N } = \mathrm { I } \mathrm { e } ^ { \mathrm { kt } }$$ N is the number of items in terms of an initial population I at a given time t and k is a growth constant equal to the percent of growth per unit time. How long will it take for the population of a
Certain country to double if its annual growth rate is 5.9%? Round to the nearest year.

Accepted Answer

A)  5 yr 
B)  1 yr 
C)  34 yr 
D)  12 yr 
A)  5 yr 
B)  1 yr 
C)  34 yr 
D)  12 yr

Question 11

Graph the function.
-$$y = \frac { 1 } { x ^ { 2 } } + 3$$

Accepted Answer

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

Question 12

Determine whether or not the graph is a graph of a function of x.
-

Accepted Answer

A)  Not a function 
B)  Function 
A)  Not a function 
B)  Function

Question 13

State the period of the function and graph.
-$$\cos \left( x + \frac { \pi } { 4 } \right)$$

Accepted Answer

A)  Period $2 \pi$
  
B)  Period $2 \pi$
  
C)  Period $2 \pi$
  
D)  $\text { Period } 2 \pi$
  
A)  Period $2 \pi$
  
B)  Period $2 \pi$
  
C)  Period $2 \pi$
  
D)  $\text { Period } 2 \pi$

Question 14

Use a graphing calculator or computer to determine which of the given viewing windows displays the most appropriate
graph of the specified function.
-$$f ( x ) = x ^ { 3 } - 2 x ^ { 2 } - 3 x + 20$$

Accepted Answer

A)  $[ - 2,2 ]$ by $[ - 10,10 ]$ 
B)  $[ - 5,5 ]$ by $[ - 5,25 ]$ 
C)  $[ - 5,25 ]$ by $[ - 5,5 ]$ 
D)  $[ - 20,20 ]$ by $[ - 100,100 ]$ 
A)  $[ - 2,2 ]$ by $[ - 10,10 ]$ 
B)  $[ - 5,5 ]$ by $[ - 5,25 ]$ 
C)  $[ - 5,25 ]$ by $[ - 5,5 ]$ 
D)  $[ - 20,20 ]$ by $[ - 100,100 ]$

Question 15

Solve the problem.
-The figure shown here shows a rectangle inscribed in an isosceles right triangle whose hypotenuse is 10 units long. Express the area A of the rectangle in terms of x.

Accepted Answer

A)  $A(x)=2 x^{2}$ 
B)  $A(x)=2 x(x-5)$ 
C)  $A(x)=x(5-x)$ 
D)  $A(x)=2 x(5-x)$ 
A)  $A(x)=2 x^{2}$ 
B)  $A(x)=2 x(x-5)$ 
C)  $A(x)=x(5-x)$ 
D)  $A(x)=2 x(5-x)$

Question 16

Find the domain and range of the inverse of the given function.
-$$f ( x ) = x ^ { 3 } + 1$$

Accepted Answer

A)  Domain: $[ 1 , \infty )$; range: all real numbers 
B)  Domain and range: all real numbers 
C)  Domain: $[ 0 , \infty )$; range: $[ 0 , \infty )$ 
D)  Domain: all real numbers; range: $[ 1 , \infty )$ 
A)  Domain: $[ 1 , \infty )$; range: all real numbers 
B)  Domain and range: all real numbers 
C)  Domain: $[ 0 , \infty )$; range: $[ 0 , \infty )$ 
D)  Domain: all real numbers; range: $[ 1 , \infty )$

Question 17

Express as a single logarithm and, if possible, simplify.
-$\ln \left( x ^ { 2 } - 25 \right) - \ln ( x + 5 )$

Accepted Answer

A)  $\ln ( x + 5 )$ 
B)  $\ln \left( x ^ { 2 } - 5 \right)$ 
C)  $\ln ( x - 25 )$ 
D)  $\ln ( x - 5 )$ 
A)  $\ln ( x + 5 )$ 
B)  $\ln \left( x ^ { 2 } - 5 \right)$ 
C)  $\ln ( x - 25 )$ 
D)  $\ln ( x - 5 )$

Question 18

Solve the problem.
-The number of acres in a landfill decreases according to the function $$B = 5300 e ^ { - 0.03 t }$$ where t is measured in years. How many acres will the landfill have after 1 years?

Accepted Answer

A)  18,585 acres 
B)  4946 acres 
C)  8071 acres 
D)  5143 acres 
A)  18,585 acres 
B)  4946 acres 
C)  8071 acres 
D)  5143 acres

Question 19

Consider the function y Can x be 0?
-For what values of $x$ is $\lceil x \rceil = 0$ ?

Accepted Answer

A)  $0 \leq x < 1$ 
B)  $- 1 < x \leq 0$ 
C)  $0 < x \leq 1$ 
D)  $- 1 \leq x < 0$ 
A)  $0 \leq x < 1$ 
B)  $- 1 < x \leq 0$ 
C)  $0 < x \leq 1$ 
D)  $- 1 \leq x < 0$

Question 20

State the domain and range of the function.
-$$f ( x ) = \frac { 5 } { 9 + e ^ { x } }$$

Accepted Answer

A)  domain: $( - \infty , \infty )$; range: $\left( 0 , \frac { 5 } { 9 } \right)$ 
B)  domain: $( 0 , \infty )$; range: $( 0 , \infty )$ 
C)  domain: $( - \infty , \infty )$; range: $( - \infty , \infty )$ 
D)  domain: $( - \infty , \infty )$; range: $( 0,9 )$ 
A)  domain: $( - \infty , \infty )$; range: $\left( 0 , \frac { 5 } { 9 } \right)$ 
B)  domain: $( 0 , \infty )$; range: $( 0 , \infty )$ 
C)  domain: $( - \infty , \infty )$; range: $( - \infty , \infty )$ 
D)  domain: $( - \infty , \infty )$; range: $( 0,9 )$

Determine if the function is even, odd, or neither. - $f ( x ) = - 8 x ^ { 5 } + 3 x ^ { 3 }$

Use the laws of exponents to simplify. Do not use negative exponents in your answer. - $\frac { 2 ^ { - 7 } } { 2 ^ { 3 } }$

Solve for the angle , where 0 2 - $\sin 2 \theta + \cos \theta = 0$

Use a graphing calculator or computer to determine which of the given viewing windows displays the most appropriate graph of the specified function. - $f ( x ) = \frac { x ^ { 2 } - 1 } { x ^ { 2 } + 1 }$

Find the exact function value. - $\sin ^ { - 1 } ( 0 )$

State the period of the function and graph. - $\cos \left(x-\frac{\pi}{4}\right)+3$ $State the period of the function and graph. - \cos \left(x-\frac{\pi}{4}\right)+3$

Determine if the function is even, odd, or neither. - $f ( x ) = ( x + 5 ) ( x + 8 )$

Find the inverse of the function. - $f ( x ) = \sqrt { x + 9 }$

Is the function graphed below one-to-one? -

Graph the function. - $y = \frac { 1 } { x ^ { 2 } } + 3$ $Graph the function. - y = \frac { 1 } { x ^ { 2 } } + 3$

Determine whether or not the graph is a graph of a function of x. -

State the period of the function and graph. - $\cos \left( x + \frac { \pi } { 4 } \right)$ $State the period of the function and graph. - \cos \left( x + \frac { \pi } { 4 } \right)$

Use a graphing calculator or computer to determine which of the given viewing windows displays the most appropriate graph of the specified function. - $f ( x ) = x ^ { 3 } - 2 x ^ { 2 } - 3 x + 20$

Solve the problem. -The figure shown here shows a rectangle inscribed in an isosceles right triangle whose hypotenuse is 10 units long. Express the area A of the rectangle in terms of x.

Find the domain and range of the inverse of the given function. - $f ( x ) = x ^ { 3 } + 1$

Express as a single logarithm and, if possible, simplify. - $\ln \left( x ^ { 2 } - 25 \right) - \ln ( x + 5 )$

Solve the problem. -The number of acres in a landfill decreases according to the function $B = 5300 e ^ { - 0.03 t }$ where t is measured in years. How many acres will the landfill have after 1 years?

Consider the function y Can x be 0? -For what values of $x$ is $\lceil x \rceil = 0$ ?

State the domain and range of the function. - $f ( x ) = \frac { 5 } { 9 + e ^ { x } }$

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

Determine if the function is even, odd, or neither. - f(x)=−8x5+3x3f ( x ) = - 8 x ^ { 5 } + 3 x ^ { 3 }f(x)=−8x5+3x3

Use the laws of exponents to simplify. Do not use negative exponents in your answer. - 2−723\frac { 2 ^ { - 7 } } { 2 ^ { 3 } }232−7​

Solve for the angle , where 0 2 - sin⁡2θ+cos⁡θ=0\sin 2 \theta + \cos \theta = 0sin2θ+cosθ=0

Use a graphing calculator or computer to determine which of the given viewing windows displays the most appropriate graph of the specified function. - f(x)=x2−1x2+1f ( x ) = \frac { x ^ { 2 } - 1 } { x ^ { 2 } + 1 }f(x)=x2+1x2−1​

Find the exact function value. - sin⁡−1(0)\sin ^ { - 1 } ( 0 )sin−1(0)

State the period of the function and graph. - cos⁡(x−π4)+3\cos \left(x-\frac{\pi}{4}\right)+3cos(x−4π​)+3

Determine if the function is even, odd, or neither. - f(x)=(x+5)(x+8)f ( x ) = ( x + 5 ) ( x + 8 )f(x)=(x+5)(x+8)

Find the inverse of the function. - f(x)=x+9f ( x ) = \sqrt { x + 9 }f(x)=x+9​