Question 1

State the period of the function:​ $$y = \sec 8 x$$ ​

Accepted Answer

A)  $\frac { \pi } { 8 }$ 
B)  $\frac { \pi } { 4 }$ ​ 
C)  $\frac { \pi } { 6 }$ ​ 
D)  $\frac { \pi } { 5 }$ ​ 
E)  $\frac { \pi } { 7 }$ ​ 
A)  $\frac { \pi } { 8 }$ 
B)  $\frac { \pi } { 4 }$ ​ 
C)  $\frac { \pi } { 6 }$ ​ 
D)  $\frac { \pi } { 5 }$ ​ 
E)  $\frac { \pi } { 7 }$ ​

Question 2

Describe the behavior of the function below as x approaches zero.​ $$f ( x ) = \frac { | x | } { 3 } \sin x$$ ​

Accepted Answer

A) f → -∞ as x → 0. 
B) f → -1 as x → 0. 
C) f → 1 as x → 0. 
D) f → +∞ as x → 0. 
E) f → 0 as x → 0. 
A) f → -∞ as x → 0. 
B) f → -1 as x → 0. 
C) f → 1 as x → 0. 
D) f → +∞ as x → 0. 
E) f → 0 as x → 0.

Question 3

Determine which of the graphs below represents ​​ $$y = | x \sin x |$$ ​

Accepted Answer

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

Question 4

Use a graphing utility to select the graph of the function:​ $$y = \frac { 1 } { 4 } \sec \left( \frac { \pi x } { 2 } + \frac { \pi } { 2 } \right)$$ ​

Accepted Answer

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

Question 5

Use a graphing utility to select the graph of the function:​ $$y = 0.3 \tan \left( \frac { \pi x } { 4 } + \frac { \pi } { 4 } \right)$$ ​

Accepted Answer

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

Question 6

Select the graph of the function below.Include two full periods.​ $$y = 0.4 \csc \pi x$$ ​

Accepted Answer

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

Question 7

Describe the behavior of the function below as x approaches $$\frac { \pi } { 2 } ^ { + }$$ .​ $$f ( x ) = \tan x$$ ​

Accepted Answer

A) f → +∞ as x → $\frac { \pi } { 2 } ^ { + }$ . 
B) f → 0 as x → $\frac { \pi } { 2 } ^ { + }$ . 
C) f → -∞ as x → $\frac { \pi } { 2 } ^ { + }$ . 
D) f → 1 as x → $\frac { \pi } { 2 } ^ { + }$ . 
E) f → -1 as x → $\frac { \pi } { 2 } ^ { + }$ . 
A) f → +∞ as x → $\frac { \pi } { 2 } ^ { + }$ . 
B) f → 0 as x → $\frac { \pi } { 2 } ^ { + }$ . 
C) f → -∞ as x → $\frac { \pi } { 2 } ^ { + }$ . 
D) f → 1 as x → $\frac { \pi } { 2 } ^ { + }$ . 
E) f → -1 as x → $\frac { \pi } { 2 } ^ { + }$ .

Question 8

Use a graphing utility to select the graph of the function below and the damping factor of the function in the same viewing window.​ $$f ( x ) = 7 \cdot 2 ^ { - \frac { x } { 4 } } \cos \pi x$$ ​

Accepted Answer

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

Question 9

Select the graph of the function below.Include two full periods.​ $$y = \frac { 1 } { 3 } \sec \pi x$$ ​

Accepted Answer

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

Question 10

Use a graphing utility to select the graph the damping factor and the function below in the same viewing window.Describe the behavior of the function as x increases without bound.​ $$f ( x ) = 2 ^ { - \frac { x } { 4 } } \cos x$$

Accepted Answer

A) ​   As x → ∞,f(x)→ 0. 
B) ​   As x → ∞,f(x)→ 0. 
C)    As x → ∞,f(x)→ 0. 
D) ​   The function f(x)is unbounded as x → ∞. 
E) ​   The function f(x)is unbounded as x → ∞. 
A) ​   As x → ∞,f(x)→ 0. 
B) ​   As x → ∞,f(x)→ 0. 
C)    As x → ∞,f(x)→ 0. 
D) ​   The function f(x)is unbounded as x → ∞. 
E) ​   The function f(x)is unbounded as x → ∞.

Question 11

Select the graph of the function below.Include two full periods.​ $$y = - 2 \sec 2 x + 2$$ ​

Accepted Answer

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

Question 12

A television camera is on a reviewing platform a meters from the street on which a parade will be passing from left to right (see figure).Write the distance d from the camera to a particular unit in the parade as a function of the angle x. a = 26.

Accepted Answer

A) d = 26tan x 
B) d = 26sec x 
C) d = 26cos x 
D) d = 26cot x 
E) d = 26sin x 
A) d = 26tan x 
B) d = 26sec x 
C) d = 26cos x 
D) d = 26cot x 
E) d = 26sin x

Question 13

Describe the behavior of the function below as x approaches zero.​ $$f ( x ) = x \sin x$$ ​

Accepted Answer

A) f → 0 as x → 0. 
B) f → -1 as x → 0. 
C) f → 1 as x → 0. 
D) f → -∞ as x → 0. 
E) f → +∞ as x → 0. 
A) f → 0 as x → 0. 
B) f → -1 as x → 0. 
C) f → 1 as x → 0. 
D) f → -∞ as x → 0. 
E) f → +∞ as x → 0.

Question 14

State the period of the function:​ $$y = \frac { 1 } { 8 } \cot \pi x$$ ​

Accepted Answer

A)  $7 \pi$ 
B)  $5 \pi$ 
C)  $6 \pi$ 
D)  $\frac { \pi } { 2 }$ 
E) 1 
A)  $7 \pi$ 
B)  $5 \pi$ 
C)  $6 \pi$ 
D)  $\frac { \pi } { 2 }$ 
E) 1

Question 15

An object weighing W pounds is suspended from the ceiling by a steel spring (see figure).The weight is pulled downward (positive direction)from its equilibrium position and released.The resulting motion of the weight is described by the function​ $y = \frac { 1 } { 2 } e ^ { - \frac { t } { 4 } } \cos 2 t , t > 0$ ​ where y is the distance (in feet)and t is the time (in seconds).
Use a graphing utility to select the graph of the function.
​​   ​

Accepted Answer

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

Question 16

Use the graph shown below to determine if the function is even,odd,or neither. ​​ $$y = \sin x$$ ​

Accepted Answer

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

Question 17

Determine whether the function below is even,odd,or neither. ​​ $$f ( x ) = 4 \csc \frac { x } { 4 }$$ ​

Accepted Answer

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

Question 18

Determine whether the function below is even,odd,or neither.​ $$f ( x ) = x ^ { 3 } \csc \frac { x } { 5 }$$ ​

Accepted Answer

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

Question 19

Use a graphing utility to select the graph of the two equations in the same viewing window.Use the graphs to determine whether the expressions are equivalent.​ $\begin{array} { l } 
y _ { 1 } = 2 \sin x \csc x , \
y _ { 2 } = 2
\end{array}$ ​

Accepted Answer

A) ​   The expressions are equivalent except
Sinx = 0,y1 is undefined. 
B) ​   The expressions are equivalent except when sinx = 0,y1 is undefined. 
C) ​   The expressions are equivalent except when
Sinx = 0,y1 is undefined. 
D) ​   The expressions are equivalent except when sinx = 0,y1 is undefined. 
E) ​   The expressions are equivalent except when sinx = 0,y1 is undefined. 
A) ​   The expressions are equivalent except
Sinx = 0,y1 is undefined. 
B) ​   The expressions are equivalent except when sinx = 0,y1 is undefined. 
C) ​   The expressions are equivalent except when
Sinx = 0,y1 is undefined. 
D) ​   The expressions are equivalent except when sinx = 0,y1 is undefined. 
E) ​   The expressions are equivalent except when sinx = 0,y1 is undefined.

Question 20

Determine whether the function below is even,odd,or neither. ​
F(x)= 0.8 cot x
​

Accepted Answer

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

Exam 28: Graphs of Other Trigonometric Functions

State the period of the function:​ y=sec⁡8xy = \sec 8 xy=sec8x ​

Describe the behavior of the function below as x approaches zero.​ f(x)=∣x∣3sin⁡xf ( x ) = \frac { | x | } { 3 } \sin xf(x)=3∣x∣​sinx ​

Determine which of the graphs below represents ​​ y=∣xsin⁡x∣y = | x \sin x |y=∣xsinx∣ ​

Use a graphing utility to select the graph of the function:​ y=14sec⁡(πx2+π2)y = \frac { 1 } { 4 } \sec \left( \frac { \pi x } { 2 } + \frac { \pi } { 2 } \right)y=41​sec(2πx​+2π​) ​

Use a graphing utility to select the graph of the function:​ y=0.3tan⁡(πx4+π4)y = 0.3 \tan \left( \frac { \pi x } { 4 } + \frac { \pi } { 4 } \right)y=0.3tan(4πx​+4π​) ​

Select the graph of the function below.Include two full periods.​ y=0.4csc⁡πxy = 0.4 \csc \pi xy=0.4cscπx ​

Describe the behavior of the function below as x approaches π2+\frac { \pi } { 2 } ^ { + }2π​+ .​ f(x)=tan⁡xf ( x ) = \tan xf(x)=tanx ​

Use a graphing utility to select the graph of the function below and the damping factor of the function in the same viewing window.​ f(x)=7⋅2−x4cos⁡πxf ( x ) = 7 \cdot 2 ^ { - \frac { x } { 4 } } \cos \pi xf(x)=7⋅2−4x​cosπx ​

Select the graph of the function below.Include two full periods.​ y=13sec⁡πxy = \frac { 1 } { 3 } \sec \pi xy=31​secπx ​

Use a graphing utility to select the graph the damping factor and the function below in the same viewing window.Describe the behavior of the function as x increases without bound.​ f(x)=2−x4cos⁡xf ( x ) = 2 ^ { - \frac { x } { 4 } } \cos xf(x)=2−4x​cosx

Select the graph of the function below.Include two full periods.​ y=−2sec⁡2x+2y = - 2 \sec 2 x + 2y=−2sec2x+2 ​

A television camera is on a reviewing platform a meters from the street on which a parade will be passing from left to right (see figure).Write the distance d from the camera to a particular unit in the parade as a function of the angle x. a = 26.

Describe the behavior of the function below as x approaches zero.​ f(x)=xsin⁡xf ( x ) = x \sin xf(x)=xsinx ​

State the period of the function:​ y=18cot⁡πxy = \frac { 1 } { 8 } \cot \pi xy=81​cotπx ​

Use the graph shown below to determine if the function is even,odd,or neither. ​​ y=sin⁡xy = \sin xy=sinx ​

Determine whether the function below is even,odd,or neither. ​​ f(x)=4csc⁡x4f ( x ) = 4 \csc \frac { x } { 4 }f(x)=4csc4x​ ​

Determine whether the function below is even,odd,or neither.​ f(x)=x3csc⁡x5f ( x ) = x ^ { 3 } \csc \frac { x } { 5 }f(x)=x3csc5x​ ​

Use a graphing utility to select the graph of the two equations in the same viewing window.Use the graphs to determine whether the expressions are equivalent.​ =2xx, =2 ​

Determine whether the function below is even,odd,or neither. ​ F(x)= 0.8 cot x ​

Rectangular Coordinates

Graphs of Equations

Linear Equations in Two Variables

Functions

Analyzing Graphs of Functions

A Library of Parent Functions

Transformations of Functions

Combinations of Functions Composite Functions

Inverse Functions

Mathematical Modeling and Variation

Quadratic Functions and Models

Polynomial Functions of Higher Degree

Polynomial and Synthetic Division

Complex Numbers

Zeros of Polynomial Functions

Rational Functions

Nonlinear Inequalities

Exponential Functions and Their Graphs

Logarithmic Functions and Their Graphs

Properties of Logarithms

Exponential and Logarithmic Equations

Exponential and Logarithmic Models

Radian and Degree Measure

Trigonometric Functions The Unit Circle

Right Triangle Trigonometry

Trigonometric Functions of Any Angle

Graphs of Sine and Cosine Functions

Inverse Trigonometric Functions

Applications and Models

Using Fundamental Identities

Verifying Trigonometric Equations

Solving Trigonometric Equations

Sum and Difference Formulas

Multiple Angle and Product to Sum Formulas

Law of Sines

Law of Cosines

Vectors in the Plane

Vectors and Dot Products

Trigonometric Form of a Complex Number

Linear and Nonlinear Systems of Equations

Two Variable Linear Systems

Multivariable Linear Systems

Partial Fractions

Systems of Inequalities

Linear Programming

Matrices and Systems of Equations

Operations With Matrices

The Inverse of a Square Matrix

The Determinant of a Square Matrix

Applications of Matrices and Determinants

Sequences and Series

Arithmetic Sequences and Partial Sums

Geometric Sequences and Series

Mathematical Induction

The Binomial Theorem

Counting Principles

Probability

Lines

Introduction to Conics Parabolas

Ellipses

State the period of the function: $y = \sec 8 x$

Describe the behavior of the function below as x approaches zero. $f ( x ) = \frac { | x | } { 3 } \sin x$

Determine which of the graphs below represents $y = | x \sin x |$

Use a graphing utility to select the graph of the function: $y = \frac { 1 } { 4 } \sec \left( \frac { \pi x } { 2 } + \frac { \pi } { 2 } \right)$

Use a graphing utility to select the graph of the function: $y = 0.3 \tan \left( \frac { \pi x } { 4 } + \frac { \pi } { 4 } \right)$

Select the graph of the function below.Include two full periods. $y = 0.4 \csc \pi x$

Describe the behavior of the function below as x approaches $\frac { \pi } { 2 } ^ { + }$ . $f ( x ) = \tan x$

Use a graphing utility to select the graph of the function below and the damping factor of the function in the same viewing window. $f ( x ) = 7 \cdot 2 ^ { - \frac { x } { 4 } } \cos \pi x$

Select the graph of the function below.Include two full periods. $y = \frac { 1 } { 3 } \sec \pi x$

Use a graphing utility to select the graph the damping factor and the function below in the same viewing window.Describe the behavior of the function as x increases without bound. $f ( x ) = 2 ^ { - \frac { x } { 4 } } \cos x$

Select the graph of the function below.Include two full periods. $y = - 2 \sec 2 x + 2$

Describe the behavior of the function below as x approaches zero. $f ( x ) = x \sin x$

State the period of the function: $y = \frac { 1 } { 8 } \cot \pi x$

Use the graph shown below to determine if the function is even,odd,or neither. $y = \sin x$ $Use the graph shown below to determine if the function is even,odd,or neither. y = \sin x $

Determine whether the function below is even,odd,or neither. $f ( x ) = 4 \csc \frac { x } { 4 }$

Determine whether the function below is even,odd,or neither. $f ( x ) = x ^ { 3 } \csc \frac { x } { 5 }$

Use a graphing utility to select the graph of the two equations in the same viewing window.Use the graphs to determine whether the expressions are equivalent. =2xx, =2

Determine whether the function below is even,odd,or neither. F(x)= 0.8 cot x