Question 1

Match the graph to the function listed whose graph most resembles the one given.
-

Accepted Answer

A)  constant function 
B)  absolute value function 
C)  linear function 
D)  reciprocal function 
A)  constant function 
B)  absolute value function 
C)  linear function 
D)  reciprocal function

Question 2

Find the average rate of change for the function between the given values.
-$f ( x ) = \frac { 3 } { x + 2 } ;$ from 1 to 4

Accepted Answer

A)  $- 28$ 
B)  $- 2$ 
C)  $- \frac { 1 } { 6 }$ 
D)  $\frac { 1 } { 2 }$ 
A)  $- 28$ 
B)  $- 2$ 
C)  $- \frac { 1 } { 6 }$ 
D)  $\frac { 1 } { 2 }$

Question 3

Write the word or phrase that best completes each statement or answers the question.
-The price $\mathrm { p }$ and $\mathrm { x }$, the quantity of a certain product sold, obey the demand equation
$$p = - \frac { 1 } { 10 } x + 100 , \{ x \mid 0 \leq x \leq 1000 \}$$
a) Express the revenue $R$ as a function of $x$.
b) What is the revenue if 450 units are sold?
c) Graph the revenue function using a graphing utility.
d) What quantity $x$ maximizes revenue? What is the maximum revenue?
e) What price should the company charge to maximize revenue?

Accepted Answer

a. @#LAT-DLM&
b. @#LAT-DLM&
c.

Question 4

Write the word or phrase that best completes each statement or answers the question.
-The volume $V$ of a square-based pyramid with base sides s and height $h$ is $V = \frac { 1 } { 3 } s ^ { 2 } h$. If the height is half of the length of a base side, express the volume $V$ as a function of s.

Accepted Answer

The answer of Write the word or phrase that best...

Question 5

If y varies directly as x, find a linear function which relates them.
-$y = 18$ when $x = 21$

Accepted Answer

A)  $f ( x ) = 3 x$ 
B)  $f ( x ) = \frac { 7 } { 6 } x$ 
C)  $f ( x ) = \frac { 6 } { 7 } x$ 
D)  $f ( x ) = x - 3$ 
A)  $f ( x ) = 3 x$ 
B)  $f ( x ) = \frac { 7 } { 6 } x$ 
C)  $f ( x ) = \frac { 6 } { 7 } x$ 
D)  $f ( x ) = x - 3$

Question 6

Choose the one alternative that best completes the statement or answers the question.
Graph the function by starting with the graph of the basic function and then using the techniques of shifting,
compressing, stretching, and/or reflecting.
-$$f ( x ) = \frac { 1 } { x - 6 } + 6$$

Accepted Answer

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

Question 7

Choose the one alternative that best completes the statement or answers the question.
Graph the function by starting with the graph of the basic function and then using the techniques of shifting,
compressing, stretching, and/or reflecting.
-$f(x)=\sqrt{x+4}$

Accepted Answer

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

Question 8

For the given functions f and g, find the requested function and state its domain.
-$$f ( x ) = \sqrt { x + 7 } ; g ( x ) = \frac { 2 } { x }$$
Find $f \cdot g$.

Accepted Answer

A)  $( f \cdot g ) ( x ) = \frac { \sqrt { 2 x + 14 } } { x } ; \{ x \mid x \geq - 7 , x \neq 0 \}$ 
B)  $( f \cdot g ) ( x ) = \frac { 2 \sqrt { x + 7 } } { x } ; \{ x \mid x \geq - 7 , x \neq 0 \}$ 
C)  $( f \cdot g ) ( x ) = \sqrt { \frac { 9 } { x } } ; \{ x \mid x \neq 0 \}$ 
D)  $( f \cdot g ) ( x ) = \sqrt { \frac { 2 x + 14 } { x } } ; \{ x \mid x \geq - 7 , x \neq 0 \}$ 
A)  $( f \cdot g ) ( x ) = \frac { \sqrt { 2 x + 14 } } { x } ; \{ x \mid x \geq - 7 , x \neq 0 \}$ 
B)  $( f \cdot g ) ( x ) = \frac { 2 \sqrt { x + 7 } } { x } ; \{ x \mid x \geq - 7 , x \neq 0 \}$ 
C)  $( f \cdot g ) ( x ) = \sqrt { \frac { 9 } { x } } ; \{ x \mid x \neq 0 \}$ 
D)  $( f \cdot g ) ( x ) = \sqrt { \frac { 2 x + 14 } { x } } ; \{ x \mid x \geq - 7 , x \neq 0 \}$

Question 9

Solve the problem.
-The height s of a ball (in feet) thrown with an initial velocity of 60 feet per second from an initial height of 4 feet is given as a function of time t (in seconds) by s(t) = -16t2 + 60t + 4. What is the maximum height? Round to the
Nearest hundredth, if necessary.

Accepted Answer

A)  -37.25 ft 
B)  60.25 ft 
C)  69.63 ft 
D)  56.5 ft 
A)  -37.25 ft 
B)  60.25 ft 
C)  69.63 ft 
D)  56.5 ft

Question 10

The graph of a function is given. Decide whether it is even, odd, or neither.
-

Accepted Answer

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

Question 11

Find the average rate of change for the function between the given values.
-$$f ( x ) = 8 x ^ { 3 } + 7 x ^ { 2 } + 8 ; \text { from } - 9 \text { to } 1$$

Accepted Answer

A)  5280 
B)  $\frac { 23 } { 10 }$ 
C)  23 
D)  528 
A)  5280 
B)  $\frac { 23 } { 10 }$ 
C)  23 
D)  528

Question 12

Find the domain of the function.
-$$f ( x ) = x ^ { 2 } + 2$$

Accepted Answer

A)  $\{ x \mid x > - 2 \}$ 
B)  $\{ x \mid x z - 2 \}$ 
C)  all real numbers 
D)  $\{ x \mid x \geq - 2 \}$ 
A)  $\{ x \mid x > - 2 \}$ 
B)  $\{ x \mid x z - 2 \}$ 
C)  all real numbers 
D)  $\{ x \mid x \geq - 2 \}$

Question 13

Determine whether the equation defines y as a function of x.
-$$y = \frac { 5 x + 3 } { x + 2 }$$

Accepted Answer

A)  function 
B)  not a function 
A)  function 
B)  not a function

Question 14

The graph of a function f is given. Use the graph to answer the question.
-Find the numbers, if any, at which f has a local maximum. What are the local maxima?

Accepted Answer

A)  $\mathrm { f }$ has a local maximum at $\mathrm { x } = - \pi$ and $\pi$; the local maximum is 2 
B)  f has no local maximum 
C)  $f$ has a local maximum at $x = 0$; the local maximum is $- 2$ 
D)  $f$ has a local maximum at $- \pi$; the local maximum is 2 
A)  $\mathrm { f }$ has a local maximum at $\mathrm { x } = - \pi$ and $\pi$; the local maximum is 2 
B)  f has no local maximum 
C)  $f$ has a local maximum at $x = 0$; the local maximum is $- 2$ 
D)  $f$ has a local maximum at $- \pi$; the local maximum is 2

Question 15

Match the graph to the function listed whose graph most resembles the one given.
-

Accepted Answer

A)  reciprocal function 
B)  square function 
C)  cube function 
D)  absolute value function 
A)  reciprocal function 
B)  square function 
C)  cube function 
D)  absolute value function

Question 16

Solve.
-The power that a resistor must dissipate is jointly proportional to the square of the current flowing through the resistor and the resistance of the resistor. If a resistor needs to dissipate 20 watts of power when 2 amperes of
Current is flowing through the resistor whose resistance is 5 ohms, find the power that a resistor needs to
Dissipate when 4 amperes of current are flowing through a resistor whose resistance is 7 ohms.

Accepted Answer

A)  112 watts 
B)  28 watts 
C)  56 watts 
D)  196 watts 
A)  112 watts 
B)  28 watts 
C)  56 watts 
D)  196 watts

Question 17

Use the graph to find the intervals on which it is increasing, decreasing, or constant.
-

Accepted Answer

A)  Increasing on $( - \infty , \infty )$ 
B)  Increasing on $\left( - \pi , - \frac { \pi } { 2 } \right)$ and $\left( \frac { \pi } { 2 } , \pi \right)$; decreasing on $\left( - \frac { \pi } { 2 } , \frac { \pi } { 2 } \right)$ 
C)  Decreasing on $\left( - \pi , - \frac { \pi } { 2 } \right)$ and $\left( \frac { \pi } { 2 } , \pi \right)$; increasing on $\left( - \frac { \pi } { 2 } , \frac { \pi } { 2 } \right)$ 
D)  Decreasing on $( - \pi , 0 )$; increasing on $( 0 , \pi )$ 
A)  Increasing on $( - \infty , \infty )$ 
B)  Increasing on $\left( - \pi , - \frac { \pi } { 2 } \right)$ and $\left( \frac { \pi } { 2 } , \pi \right)$; decreasing on $\left( - \frac { \pi } { 2 } , \frac { \pi } { 2 } \right)$ 
C)  Decreasing on $\left( - \pi , - \frac { \pi } { 2 } \right)$ and $\left( \frac { \pi } { 2 } , \pi \right)$; increasing on $\left( - \frac { \pi } { 2 } , \frac { \pi } { 2 } \right)$ 
D)  Decreasing on $( - \pi , 0 )$; increasing on $( 0 , \pi )$

Question 18

Answer the question about the given function.
-Given the function $f ( x ) = x ^ { 2 } + 7 x - 18$, list the $x$-intercepts, if any, of the graph of $f$.

Accepted Answer

A)  $( - 9,0 ) , ( 2,0 )$ 
B)  $( 9,0 ) , ( 2,0 )$ 
C)  $( 9,0 ) , ( - 2,0 )$ 
D)  $( - 9,0 ) , ( 1,0 )$ 
A)  $( - 9,0 ) , ( 2,0 )$ 
B)  $( 9,0 ) , ( 2,0 )$ 
C)  $( 9,0 ) , ( - 2,0 )$ 
D)  $( - 9,0 ) , ( 1,0 )$

Question 19

For the given functions f and g, find the requested function and state its domain.
-$$f ( x ) = \frac { 7 x - 6 } { 6 x - 1 } ; g ( x ) = \frac { 4 x } { 6 x - 1 }$$
Find $f + g$.

Accepted Answer

A)  $( \mathrm { f } + \mathrm { g } ) ( \mathrm { x } ) = \frac { 11 \mathrm { x } - 6 } { 6 \mathrm { x } - 1 } ; \left\{ \mathrm { x } \mid \mathrm { x } \neq \frac { 1 } { 6 } \right\}$ 
B)  $( f + g ) ( x ) = \frac { 11 x - 6 } { 6 x - 1 } ; \{ x \mid x \neq 0 \}$ 
C)  $( f + g ) ( x ) = \frac { 11 x - 6 } { 6 x - 1 } ; \left\{ x \mid x \neq \frac { 1 } { 6 } , x \neq \frac { 6 } { 11 } \right\}$ 
D)  $( \mathrm { f } + \mathrm { g } ) ( \mathrm { x } ) = \frac { 3 \mathrm { x } + 6 } { 6 \mathrm { x } - 1 } ; \left\{ \mathrm { x } \mid \mathrm { x } \neq \frac { 1 } { 6 } \right\}$ 
A)  $( \mathrm { f } + \mathrm { g } ) ( \mathrm { x } ) = \frac { 11 \mathrm { x } - 6 } { 6 \mathrm { x } - 1 } ; \left\{ \mathrm { x } \mid \mathrm { x } \neq \frac { 1 } { 6 } \right\}$ 
B)  $( f + g ) ( x ) = \frac { 11 x - 6 } { 6 x - 1 } ; \{ x \mid x \neq 0 \}$ 
C)  $( f + g ) ( x ) = \frac { 11 x - 6 } { 6 x - 1 } ; \left\{ x \mid x \neq \frac { 1 } { 6 } , x \neq \frac { 6 } { 11 } \right\}$ 
D)  $( \mathrm { f } + \mathrm { g } ) ( \mathrm { x } ) = \frac { 3 \mathrm { x } + 6 } { 6 \mathrm { x } - 1 } ; \left\{ \mathrm { x } \mid \mathrm { x } \neq \frac { 1 } { 6 } \right\}$

Question 20

Determine whether the equation defines y as a function of x.
-$$y ^ { 2 } + x = 2$$

Accepted Answer

A)  function 
B)  not a function 
A)  function 
B)  not a function

Match the graph to the function listed whose graph most resembles the one given. -

Find the average rate of change for the function between the given values. - $f ( x ) = \frac { 3 } { x + 2 } ;$ from 1 to 4

Write the word or phrase that best completes each statement or answers the question. -The volume $V$ of a square-based pyramid with base sides s and height $h$ is $V = \frac { 1 } { 3 } s ^ { 2 } h$ . If the height is half of the length of a base side, express the volume $V$ as a function of s.

If y varies directly as x, find a linear function which relates them. - $y = 18$ when $x = 21$

For the given functions f and g, find the requested function and state its domain. - $f ( x ) = \sqrt { x + 7 } ; g ( x ) = \frac { 2 } { x }$ Find $f \cdot g$ .

Solve the problem. -The height s of a ball (in feet) thrown with an initial velocity of 60 feet per second from an initial height of 4 feet is given as a function of time t (in seconds) by s(t) = -16t2 + 60t + 4. What is the maximum height? Round to the Nearest hundredth, if necessary.

The graph of a function is given. Decide whether it is even, odd, or neither. -

Find the average rate of change for the function between the given values. - $f ( x ) = 8 x ^ { 3 } + 7 x ^ { 2 } + 8 ; \text { from } - 9 \text { to } 1$

Find the domain of the function. - $f ( x ) = x ^ { 2 } + 2$

Determine whether the equation defines y as a function of x. - $y = \frac { 5 x + 3 } { x + 2 }$

The graph of a function f is given. Use the graph to answer the question. -Find the numbers, if any, at which f has a local maximum. What are the local maxima?

Match the graph to the function listed whose graph most resembles the one given. -

Use the graph to find the intervals on which it is increasing, decreasing, or constant. -

Answer the question about the given function. -Given the function $f ( x ) = x ^ { 2 } + 7 x - 18$ , list the $x$ -intercepts, if any, of the graph of $f$ .

For the given functions f and g, find the requested function and state its domain. - $f ( x ) = \frac { 7 x - 6 } { 6 x - 1 } ; g ( x ) = \frac { 4 x } { 6 x - 1 }$ Find $f + g$ .

Determine whether the equation defines y as a function of x. - $y ^ { 2 } + x = 2$

Linear and Quadratic Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Foundations: a Prelude to Functions

Graphing Utilities

Filters

Exam 1: Functions and Their Graphs

Match the graph to the function listed whose graph most resembles the one given. -

Find the average rate of change for the function between the given values. - f(x)=3x+2;f ( x ) = \frac { 3 } { x + 2 } ;f(x)=x+23​; from 1 to 4

If y varies directly as x, find a linear function which relates them. - y=18y = 18y=18 when x=21x = 21x=21

Choose the one alternative that best completes the statement or answers the question. Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - f(x)=x+4f(x)=\sqrt{x+4}f(x)=x+4​

For the given functions f and g, find the requested function and state its domain. - f(x)=x+7;g(x)=2xf ( x ) = \sqrt { x + 7 } ; g ( x ) = \frac { 2 } { x }f(x)=x+7​;g(x)=x2​ Find f⋅gf \cdot gf⋅g .

Solve the problem. -The height s of a ball (in feet) thrown with an initial velocity of 60 feet per second from an initial height of 4 feet is given as a function of time t (in seconds) by s(t) = -16t2 + 60t + 4. What is the maximum height? Round to the Nearest hundredth, if necessary.

The graph of a function is given. Decide whether it is even, odd, or neither. -

Find the average rate of change for the function between the given values. - f(x)=8x3+7x2+8; from −9 to 1f ( x ) = 8 x ^ { 3 } + 7 x ^ { 2 } + 8 ; \text { from } - 9 \text { to } 1f(x)=8x3+7x2+8; from −9 to 1

Find the domain of the function. - f(x)=x2+2f ( x ) = x ^ { 2 } + 2f(x)=x2+2

Determine whether the equation defines y as a function of x. - y=5x+3x+2y = \frac { 5 x + 3 } { x + 2 }y=x+25x+3​

The graph of a function f is given. Use the graph to answer the question. -Find the numbers, if any, at which f has a local maximum. What are the local maxima?

Match the graph to the function listed whose graph most resembles the one given. -

Use the graph to find the intervals on which it is increasing, decreasing, or constant. -

Answer the question about the given function. -Given the function f(x)=x2+7x−18f ( x ) = x ^ { 2 } + 7 x - 18f(x)=x2+7x−18 , list the xxx -intercepts, if any, of the graph of fff .

For the given functions f and g, find the requested function and state its domain. - f(x)=7x−66x−1;g(x)=4x6x−1f ( x ) = \frac { 7 x - 6 } { 6 x - 1 } ; g ( x ) = \frac { 4 x } { 6 x - 1 }f(x)=6x−17x−6​;g(x)=6x−14x​ Find f+gf + gf+g .

Determine whether the equation defines y as a function of x. - y2+x=2y ^ { 2 } + x = 2y2+x=2

Linear and Quadratic Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Foundations: a Prelude to Functions

Graphing Utilities

Filters

Find the average rate of change for the function between the given values. - $f ( x ) = \frac { 3 } { x + 2 } ;$ from 1 to 4

If y varies directly as x, find a linear function which relates them. - $y = 18$ when $x = 21$

For the given functions f and g, find the requested function and state its domain. - $f ( x ) = \sqrt { x + 7 } ; g ( x ) = \frac { 2 } { x }$ Find $f \cdot g$ .

Find the average rate of change for the function between the given values. - $f ( x ) = 8 x ^ { 3 } + 7 x ^ { 2 } + 8 ; \text { from } - 9 \text { to } 1$

Find the domain of the function. - $f ( x ) = x ^ { 2 } + 2$

Determine whether the equation defines y as a function of x. - $y = \frac { 5 x + 3 } { x + 2 }$

Answer the question about the given function. -Given the function $f ( x ) = x ^ { 2 } + 7 x - 18$ , list the $x$ -intercepts, if any, of the graph of $f$ .

For the given functions f and g, find the requested function and state its domain. - $f ( x ) = \frac { 7 x - 6 } { 6 x - 1 } ; g ( x ) = \frac { 4 x } { 6 x - 1 }$ Find $f + g$ .

Determine whether the equation defines y as a function of x. - $y ^ { 2 } + x = 2$