Question 1

For the given functions f and g, find the requested function and state its domain.
-$f ( x ) = 3 - 2 x ; g ( x ) = - 9 x + 2$ Find f + g.

Accepted Answer

A)  $( f + g ) ( x ) = 7 x + 5 ; \left\{ x \mid x \neq \frac { 5 } { 7 } \right\}$ 
B)  $( f + g ) ( x ) = - 11 x + 5 ;$ all real numbers 
C) $ ( f + g ) ( x ) = - 6 x ;$ all real numbers 
D)  $( f + g ) ( x ) = - 9 x + 3 ; \left\{ x \mid x \neq \frac { 1 } { 3 } \right\}$ 
A)  $( f + g ) ( x ) = 7 x + 5 ; \left\{ x \mid x \neq \frac { 5 } { 7 } \right\}$ 
B)  $( f + g ) ( x ) = - 11 x + 5 ;$ all real numbers 
C) $ ( f + g ) ( x ) = - 6 x ;$ all real numbers 
D)  $( f + g ) ( x ) = - 9 x + 3 ; \left\{ x \mid x \neq \frac { 1 } { 3 } \right\}$

Question 2

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-4)3

Accepted Answer

A) 
  
B) 
  
C) 
  
D)

Question 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?

Accepted Answer

A)  f has a local maximum at x = 2; the local maximum is 1 
B)  f has a local maximum at x = -2 and 2; the local maximum is 0 
C)  f has a local maximum at x = 0; the local maximum is 1 
D)  f has no local maximum 
A)  f has a local maximum at x = 2; the local maximum is 1 
B)  f has a local maximum at x = -2 and 2; the local maximum is 0 
C)  f has a local maximum at x = 0; the local maximum is 1 
D)  f has no local maximum

Question 4

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 5

Graph the function by starting with the graph of the basic function and then using the techniques of shifting,
compressing, stretching, and/or reflecting.
- $f(x)= 4| x |$

Accepted Answer

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

Question 6

Solve the problem.
-The concentration C (arbitrary units) of a certain drug in a patient's bloodstream can be modeled using where t is the number of hours since a 500 milligram oral dose was administered. Using $$C ( t ) = \frac { t } { ( 0.542 t + 1.844 ) ^ { 2 } }$$ the TABLE feature of a graphing utility, find the time at which the concentration of the drug is greatest. Round
To the nearest tenth of an hour.

Accepted Answer

A)  4.9 hours 
B)  4.2 hours 
C)  5.7 hours 
D)  3.4 hours 
A)  4.9 hours 
B)  4.2 hours 
C)  5.7 hours 
D)  3.4 hours

Question 7

Determine whether the equation defines y as a function of x.
-$$x ^ { 2 } - 4 y ^ { 2 } = 1$$

Accepted Answer

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

Question 8

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) =-x2

Accepted Answer

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

Question 9

Solve the problem.
-An electric company has the following rate schedule for electricity usage in single-family residences:

What is the charge for using 300 kilowatts in one month?
What is the charge for using 375 kilowatts in one month?
Construct a function that gives the monthly charge C for x kilowatts of electricity.

Accepted Answer

$39.70
$49.69 \[C ( x ) = \lef

Question 10

Solve the problem.
-$$\text { If } f ( x ) = \frac { x - 5 A } { - 10 x + 2 }$$

Accepted Answer

A)  A = 100 
B)  A = -104 
C)  A = 104 
D)  A = -100 
A)  A = 100 
B)  A = -104 
C)  A = 104 
D)  A = -100

Question 11

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) =-x3

Accepted Answer

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

Question 12

Graph the function by starting with the graph of the basic function and then using the techniques of shifting,
compressing, stretching, and/or reflecting.
-$f(x)=\frac{6}{x}$

Accepted Answer

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

Question 13

Graph the function by starting with the graph of the basic function and then using the techniques of shifting,
compressing, stretching, and/or reflecting.
-$f ( x ) = \frac { 1 } { 4 } | x |$

Accepted Answer

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

Question 14

Graph the function by starting with the graph of the basic function and then using the techniques of shifting,
compressing, stretching, and/or reflecting.
-$f(x)=\frac{1}{7} x^{2}$

Accepted Answer

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

Question 15

Graph the function by starting with the graph of the basic function and then using the techniques of shifting,
compressing, stretching, and/or reflecting.
-$f(x)=5 \sqrt{x}$

Accepted Answer

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

Question 16

Solve the problem.
-$\text { Given } f ( x ) = \frac { 1 } { x } \text { and } \left( \frac { f } { g } \right) ( x ) = \frac { x - 4 } { x ^ { 2 } - 6 x } \text {, find the function } g \text {. }$

Accepted Answer

A)  $g ( x ) = \frac { x + 4 } { x + 6 }$ 
B)  $g ( x ) = \frac { x + 6 } { x + 4 }$ 
C)  $g ( x ) = \frac { x - 4 } { x - 6 }$ 
D)  $g ( x ) = \frac { x - 6 } { x - 4 }$ 
A)  $g ( x ) = \frac { x + 4 } { x + 6 }$ 
B)  $g ( x ) = \frac { x + 6 } { x + 4 }$ 
C)  $g ( x ) = \frac { x - 4 } { x - 6 }$ 
D)  $g ( x ) = \frac { x - 6 } { x - 4 }$

Question 17

Find an equation of the secant line containing (1, f(1)) and (2, f(2)).
-$$f ( x ) = x ^ { 3 } - x$$

Accepted Answer

A)  y = -6x + 6 
B)  y = 6x - 6 
C)  y = 6x + 6 
D)  y = -6x - 6 
A)  y = -6x + 6 
B)  y = 6x - 6 
C)  y = 6x + 6 
D)  y = -6x - 6

Question 18

Solve the problem.
-Sue wants to put a rectangular garden on her property using 70 meters of fencing. There is a river that runs through her property so she decides to increase the size of the garden by using the river as one side of the
Rectangle. (Fencing is then needed only on the other three sides.) Let x represent the length of the side of the
Rectangle along the river. Express the garden's area as a function of x.

Accepted Answer

A)  $A ( x ) = 35 x - \frac { 1 } { 2 } x ^ { 2 }$ 
B)  $A ( x ) = 34 x - \frac { 1 } { 4 } x ^ { 2 }$ 
C)  $A ( x ) = 35 x ^ { 2 } - x$ 
D)  $A ( x ) = 36 x - 2 x ^ { 2 }$ 
A)  $A ( x ) = 35 x - \frac { 1 } { 2 } x ^ { 2 }$ 
B)  $A ( x ) = 34 x - \frac { 1 } { 4 } x ^ { 2 }$ 
C)  $A ( x ) = 35 x ^ { 2 } - x$ 
D)  $A ( x ) = 36 x - 2 x ^ { 2 }$

Question 19

Find the average rate of change for the function between the given values.
-$f ( x ) = \frac { 3 } { x - 2 } ; \text { from } 4 \text { to } 7$

Accepted Answer

A)  $- \frac { 3 } { 10 }$ 
B)  $\frac { 1 } { 3 }$ 
C)  2 
D)  7 
A)  $- \frac { 3 } { 10 }$ 
B)  $\frac { 1 } { 3 }$ 
C)  2 
D)  7

Question 20

Answer the question about the given function.
-Given the functi $$f ( x ) = - 2 x ^ { 2 } + 4 x + 3$$ , is the point (2, -1) on the graph of f?

Accepted Answer

A)  Yes 
B)  No 
A)  Yes 
B)  No

For the given functions f and g, find the requested function and state its domain. - $f ( x ) = 3 - 2 x ; g ( x ) = - 9 x + 2$ Find f + g.

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-4)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?

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

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - $f(x)= 4| x |$

Determine whether the equation defines y as a function of x. - $x ^ { 2 } - 4 y ^ { 2 } = 1$

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) =-x²

Solve the problem. - $\text { If } f ( x ) = \frac { x - 5 A } { - 10 x + 2 }$

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) =-x³

Solve the problem. - $\text { Given } f ( x ) = \frac { 1 } { x } \text { and } \left( \frac { f } { g } \right) ( x ) = \frac { x - 4 } { x ^ { 2 } - 6 x } \text {, find the function } g \text {. }$

Find an equation of the secant line containing (1, f(1)) and (2, f(2)). - $f ( x ) = x ^ { 3 } - x$

Find the average rate of change for the function between the given values. - $f ( x ) = \frac { 3 } { x - 2 } ; \text { from } 4 \text { to } 7$

Answer the question about the given function. -Given the functi $f ( x ) = - 2 x ^ { 2 } + 4 x + 3$ , is the point (2, -1) on the graph of f?

Linear and Quadratic Functions

Polynomial and Rational Functions

Conics

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

Filters

Exam 1: Functions and Their Graphs

For the given functions f and g, find the requested function and state its domain. - f(x)=3−2x;g(x)=−9x+2f ( x ) = 3 - 2 x ; g ( x ) = - 9 x + 2f(x)=3−2x;g(x)=−9x+2 Find f + g.

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-4)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?

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

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)=4∣x∣f(x)= 4| x |f(x)=4∣x∣

Determine whether the equation defines y as a function of x. - x2−4y2=1x ^ { 2 } - 4 y ^ { 2 } = 1x2−4y2=1

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) =-x2

Solve the problem. - If f(x)=x−5A−10x+2\text { If } f ( x ) = \frac { x - 5 A } { - 10 x + 2 } If f(x)=−10x+2x−5A​

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) =-x3

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)=6xf(x)=\frac{6}{x}f(x)=x6​

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)=14∣x∣f ( x ) = \frac { 1 } { 4 } | x |f(x)=41​∣x∣

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)=17x2f(x)=\frac{1}{7} x^{2}f(x)=71​x2

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)=5xf(x)=5 \sqrt{x}f(x)=5x​

Find an equation of the secant line containing (1, f(1)) and (2, f(2)). - f(x)=x3−xf ( x ) = x ^ { 3 } - xf(x)=x3−x

Find the average rate of change for the function between the given values. - f(x)=3x−2; from 4 to 7f ( x ) = \frac { 3 } { x - 2 } ; \text { from } 4 \text { to } 7f(x)=x−23​; from 4 to 7

Answer the question about the given function. -Given the functi f(x)=−2x2+4x+3f ( x ) = - 2 x ^ { 2 } + 4 x + 3f(x)=−2x2+4x+3 , is the point (2, -1) on the graph of f?

Linear and Quadratic Functions

Polynomial and Rational Functions

Conics

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

Filters

For the given functions f and g, find the requested function and state its domain. - $f ( x ) = 3 - 2 x ; g ( x ) = - 9 x + 2$ Find f + g.

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-4)³

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - $f(x)= 4| x |$

Determine whether the equation defines y as a function of x. - $x ^ { 2 } - 4 y ^ { 2 } = 1$

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) =-x²

Solve the problem. - $\text { If } f ( x ) = \frac { x - 5 A } { - 10 x + 2 }$

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) =-x³

Find an equation of the secant line containing (1, f(1)) and (2, f(2)). - $f ( x ) = x ^ { 3 } - x$

Find the average rate of change for the function between the given values. - $f ( x ) = \frac { 3 } { x - 2 } ; \text { from } 4 \text { to } 7$

Answer the question about the given function. -Given the functi $f ( x ) = - 2 x ^ { 2 } + 4 x + 3$ , is the point (2, -1) on the graph of f?