Question 1

For the graph of the function y = f(x), find the absolute maximum and the absolute minimum, if it exists.
-

Accepted Answer

A)  Absolute maximum: none; Absolute minimum: f(1) = 2 
B)  Absolute maximum: none; Absolute minimum: none 
C)  Absolute maximum: f(4) = 7; Absolute minimum: none 
D)  Absolute maximum: f(4) = 7; Absolute minimum: f(1) = 2 
A)  Absolute maximum: none; Absolute minimum: f(1) = 2 
B)  Absolute maximum: none; Absolute minimum: none 
C)  Absolute maximum: f(4) = 7; Absolute minimum: none 
D)  Absolute maximum: f(4) = 7; Absolute minimum: f(1) = 2

Question 2

Solve the problem.
-A wire 20 feet long is to be cut into two pieces. One piece will be shaped as a square and the other piece will be shaped as an equilateral triangle. Express the total area A enclosed by the pieces of wire as a function of the length x of a side of the equilateral triangle. What is the domain of A?

Accepted Answer

The answer of Solve the problem.
-A wire 20 feet long...

Question 3

Find and simplify the difference quotient of f $\frac { f ( x + h ) - f ( x ) } { h }$ , h ≠ 0, for the function.
-$( x ) = \frac { 1 } { 7 x }$

Accepted Answer

A)  $\frac { - 1 } { x ( x + h ) }$ 
B)  $\frac { 1 } { 7 x }$ 
C)  0 
D)  $\frac { - 1 } { 7 x ( x + h ) }$ 
A)  $\frac { - 1 } { x ( x + h ) }$ 
B)  $\frac { 1 } { 7 x }$ 
C)  0 
D)  $\frac { - 1 } { 7 x ( x + h ) }$

Question 4

Graph the function by starting with the graph of the basic function and then using the techniques of shifting,
compressing, stretching, and/or reflecting.
-

Accepted Answer

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

Question 5

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given
interval.
-(-6, -2.5)

Accepted Answer

A)  constant 
B)  decreasing 
C)  increasing 
A)  constant 
B)  decreasing 
C)  increasing

Question 6

Determine algebraically whether the function is even, odd, or neither.
-$$f ( x ) = - 2 x ^ { 4 } - x ^ { 2 }$$

Accepted Answer

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

Question 7

Graph the function by starting with the graph of the basic function and then using the techniques of shifting,
compressing, stretching, and/or reflecting.
-$f ( x ) = 3 ( x + 1 ) ^ { 2 } - 3$

Accepted Answer

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

Question 8

Graph the function.
-f(x) = x

Accepted Answer

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

Question 9

Determine algebraically whether the function is even, odd, or neither.
-$$f ( x ) = \frac { 1 } { x ^ { 2 } }$$

Accepted Answer

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

Question 10

The graph of a function f is given. Use the graph to answer the question.
-What is the y-intercept?

Accepted Answer

A)  50 
B)  -30 
C)  -40 
D)  35 
A)  50 
B)  -30 
C)  -40 
D)  35

Question 11

Answer the question about the given function.
-Given the functi $$f ( x ) = - 6 x ^ { 2 } + 12 x - 9$$ , if x = 1, what is f(x)? What point is on the graph of f?

Accepted Answer

A)  -3; (1, -3) 
B)  -3; (-3, 1) 
C)  -27; (1, -27) 
D)  -27; (-27, 1) 
A)  -3; (1, -3) 
B)  -3; (-3, 1) 
C)  -27; (1, -27) 
D)  -27; (-27, 1)

Question 12

Find the value for the function.
-Find f( $( x + h ) \text { when } f ( x ) = 2 x ^ { 2 } - 2 x - 5$

Accepted Answer

A)  $2 x ^ { 2 } + 2 x h + 2 h ^ { 2 } - 2 x - 2 h - 5$ 
B)  $2 x ^ { 2 } + 4 x h + 2 h ^ { 2 } - 2 x - 2 h - 5$ 
C)  $2 x ^ { 2 } + 2 h ^ { 2 } + 2 x + 2 h - 5$ 
D)  $2 x ^ { 2 } + 2 h ^ { 2 } - 2 x - 2 h - 5$ 
A)  $2 x ^ { 2 } + 2 x h + 2 h ^ { 2 } - 2 x - 2 h - 5$ 
B)  $2 x ^ { 2 } + 4 x h + 2 h ^ { 2 } - 2 x - 2 h - 5$ 
C)  $2 x ^ { 2 } + 2 h ^ { 2 } + 2 x + 2 h - 5$ 
D)  $2 x ^ { 2 } + 2 h ^ { 2 } - 2 x - 2 h - 5$

Question 13

Solve the problem.
-The height s of a ball (in feet) thrown with an initial velocity of 70 feet per second from an initial height of 3 feet is given as a function of time t (in seconds) by s(t) = -16t2 + 70t + 3. What is the maximum height? Round to the
Nearest hundredth, if necessary.

Accepted Answer

A)  -54.5 ft 
B)  79.56 ft 
C)  76.75 ft 
D)  90.5 ft 
A)  -54.5 ft 
B)  79.56 ft 
C)  76.75 ft 
D)  90.5 ft

Question 14

Find the value for the function.
-$f ( x + h ) \text { when } f ( x ) = \frac { - 3 x + 8 } { 7 x - 9 }$

Accepted Answer

A)  $\frac { - 3 x - 3 h + 8 } { 7 x - 9 }$ 
B)  $\frac { - 3 x + 5 h } { 7 x - 2 h }$ 
C)  $\frac { - 3 x + 8 h } { 7 x - 9 h }$ 
D)  $\frac { - 3 x - 3 h + 8 } { 7 x + 7 h - 9 }$ 
A)  $\frac { - 3 x - 3 h + 8 } { 7 x - 9 }$ 
B)  $\frac { - 3 x + 5 h } { 7 x - 2 h }$ 
C)  $\frac { - 3 x + 8 h } { 7 x - 9 h }$ 
D)  $\frac { - 3 x - 3 h + 8 } { 7 x + 7 h - 9 }$

Question 15

The graph of a piecewise-defined function is given. Write a definition for the function.
-

Accepted Answer

A) 
$f ( x ) = \left\{ \begin{array} { l l } \frac { 3 } { 4 } x + 4 & \text { if } - 3 \leq x \leq 0 \ \frac { 3 } { 2 } x & \text { if } x \geq 0 \end{array} \right.$ 
B) 
$f ( x ) = \left\{ \begin{array} { l l } \frac { 3 } { 4 } x + 4 & \text { if } - 3 \leq x \leq 0 \ \frac { 3 } { 2 } x & \text { if } x > 0 \end{array} \right.$ 
C) 
$$f ( x ) = \left\{ \begin{array} { l l } 
\frac { 4 } { 3 } x + 4 & \text { if } - 3 \leq x \leq 0 \
\frac { 2 } { 3 } x & \text { if } 0  0
\end{array} \right. \right.$$ 
A) 
$f ( x ) = \left\{ \begin{array} { l l } \frac { 3 } { 4 } x + 4 & \text { if } - 3 \leq x \leq 0 \ \frac { 3 } { 2 } x & \text { if } x \geq 0 \end{array} \right.$ 
B) 
$f ( x ) = \left\{ \begin{array} { l l } \frac { 3 } { 4 } x + 4 & \text { if } - 3 \leq x \leq 0 \ \frac { 3 } { 2 } x & \text { if } x > 0 \end{array} \right.$ 
C) 
$$f ( x ) = \left\{ \begin{array} { l l } 
\frac { 4 } { 3 } x + 4 & \text { if } - 3 \leq x \leq 0 \
\frac { 2 } { 3 } x & \text { if } 0  0
\end{array} \right. \right.$$

Question 16

Find the function.
-Find the function that is finally graphed after the following transformations are applied to the graph of y = |x|. The graph is shifted right 3 units, stretched by a factor of 3, shifted vertically down 2 units, and finally reflected
Across the x-axis.

Accepted Answer

A)  $y = - ( 3 | x + 3 | - 2 )$ 
B)  $y = - ( 3 | x - 3 | - 2 )$ 
C)  $y = - 3 | x - 3 | - 2$ 
D)  $y = 3 | - x - 3 | - 2$ 
A)  $y = - ( 3 | x + 3 | - 2 )$ 
B)  $y = - ( 3 | x - 3 | - 2 )$ 
C)  $y = - 3 | x - 3 | - 2$ 
D)  $y = 3 | - x - 3 | - 2$

Question 17

Given the functi is the point (-1, 4) on the graph of f?
-$$f ( x ) = \frac { x ^ { 2 } - 3 } { x + 2 }$$

Accepted Answer

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

Question 18

Find and simplify the difference quotient of f $\frac { f ( x + h ) - f ( x ) } { h }$ , h ≠ 0, for the function.
-$$f ( x ) = x ^ { 2 } + 6 x - 8$$

Accepted Answer

A)  2x+ h - 8 
B)  $$\frac { 2 x ^ { 2 } + 2 x + 2 x h + h ^ { 2 } + h - 16 } { h }$$ 
C)  1 
D)  2x+ h + 6 
A)  2x+ h - 8 
B)  $$\frac { 2 x ^ { 2 } + 2 x + 2 x h + h ^ { 2 } + h - 16 } { h }$$ 
C)  1 
D)  2x+ h + 6

Question 19

Find the domain of the function.
-$$h ( x ) = \frac { x - 1 } { x ^ { 3 } - 25 x }$$

Accepted Answer

A)  {x|x ≠-5, 0, 5} 
B)  {x|x ≠ 0} 
C)  all real numbers 
D)  {x|x ≠1} 
A)  {x|x ≠-5, 0, 5} 
B)  {x|x ≠ 0} 
C)  all real numbers 
D)  {x|x ≠1}

Question 20

Use a graphing utility to graph the function over the indicated interval and approximate any local maxima and local
minima. If necessary, round answers to two decimal places.
-$f ( x ) = x ^ { 4 } - 5 x ^ { 3 } + 3 x ^ { 2 } + 9 x - 3 ; ( - 5,5 )$

Accepted Answer

A) local minimum at (-3, -3)
local maximum at (-1.32, 5.64)
local minimum at (0.57, -6.12) 
B) local minimum at (-0.57, -6.12)
local maximum at (1.32, 5.64)
local minimum at (3, -3) 
C) local minimum at (-0.61, -5.64)
local maximum at (1.41, 6.12)
local minimum at (3, -3) 
D) local minimum at (-1, -6)
local maximum at (1, 6)
local minimum at (3, -3) 
A) local minimum at (-3, -3)
local maximum at (-1.32, 5.64)
local minimum at (0.57, -6.12) 
B) local minimum at (-0.57, -6.12)
local maximum at (1.32, 5.64)
local minimum at (3, -3) 
C) local minimum at (-0.61, -5.64)
local maximum at (1.41, 6.12)
local minimum at (3, -3) 
D) local minimum at (-1, -6)
local maximum at (1, 6)
local minimum at (3, -3)

For the graph of the function y = f(x), find the absolute maximum and the absolute minimum, if it exists. -

Find and simplify the difference quotient of f $\frac { f ( x + h ) - f ( x ) } { h }$ , h ≠ 0, for the function. - $( x ) = \frac { 1 } { 7 x }$

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. -

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. -(-6, -2.5)

Determine algebraically whether the function is even, odd, or neither. - $f ( x ) = - 2 x ^ { 4 } - x ^ { 2 }$

Graph the function. -f(x) = x

Determine algebraically whether the function is even, odd, or neither. - $f ( x ) = \frac { 1 } { x ^ { 2 } }$

The graph of a function f is given. Use the graph to answer the question. -What is the y-intercept?

Answer the question about the given function. -Given the functi $f ( x ) = - 6 x ^ { 2 } + 12 x - 9$ , if x = 1, what is f(x)? What point is on the graph of f?

Find the value for the function. -Find f( $( x + h ) \text { when } f ( x ) = 2 x ^ { 2 } - 2 x - 5$

Solve the problem. -The height s of a ball (in feet) thrown with an initial velocity of 70 feet per second from an initial height of 3 feet is given as a function of time t (in seconds) by s(t) = -16t² + 70t + 3. What is the maximum height? Round to the Nearest hundredth, if necessary.

Find the value for the function. - $f ( x + h ) \text { when } f ( x ) = \frac { - 3 x + 8 } { 7 x - 9 }$

The graph of a piecewise-defined function is given. Write a definition for the function. -

Find the function. -Find the function that is finally graphed after the following transformations are applied to the graph of y = |x|. The graph is shifted right 3 units, stretched by a factor of 3, shifted vertically down 2 units, and finally reflected Across the x-axis.

Given the functi is the point (-1, 4) on the graph of f? - $f ( x ) = \frac { x ^ { 2 } - 3 } { x + 2 }$

Find and simplify the difference quotient of f $\frac { f ( x + h ) - f ( x ) } { h }$ , h ≠ 0, for the function. - $f ( x ) = x ^ { 2 } + 6 x - 8$

Find the domain of the function. - $h ( x ) = \frac { x - 1 } { x ^ { 3 } - 25 x }$

Use a graphing utility to graph the function over the indicated interval and approximate any local maxima and local minima. If necessary, round answers to two decimal places. - $f ( x ) = x ^ { 4 } - 5 x ^ { 3 } + 3 x ^ { 2 } + 9 x - 3 ; ( - 5,5 )$

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 graph of the function y = f(x), find the absolute maximum and the absolute minimum, if it exists. -

Find and simplify the difference quotient of f f(x+h)−f(x)h\frac { f ( x + h ) - f ( x ) } { h }hf(x+h)−f(x)​ , h ≠ 0, for the function. - (x)=17x( x ) = \frac { 1 } { 7 x }(x)=7x1​

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. -

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. -(-6, -2.5)

Determine algebraically whether the function is even, odd, or neither. - f(x)=−2x4−x2f ( x ) = - 2 x ^ { 4 } - x ^ { 2 }f(x)=−2x4−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)=3(x+1)2−3f ( x ) = 3 ( x + 1 ) ^ { 2 } - 3f(x)=3(x+1)2−3

Graph the function. -f(x) = x

Determine algebraically whether the function is even, odd, or neither. - f(x)=1x2f ( x ) = \frac { 1 } { x ^ { 2 } }f(x)=x21​

The graph of a function f is given. Use the graph to answer the question. -What is the y-intercept?

Answer the question about the given function. -Given the functi f(x)=−6x2+12x−9f ( x ) = - 6 x ^ { 2 } + 12 x - 9f(x)=−6x2+12x−9 , if x = 1, what is f(x)? What point is on the graph of f?

Find the value for the function. -Find f( (x+h) when f(x)=2x2−2x−5( x + h ) \text { when } f ( x ) = 2 x ^ { 2 } - 2 x - 5(x+h) when f(x)=2x2−2x−5

Solve the problem. -The height s of a ball (in feet) thrown with an initial velocity of 70 feet per second from an initial height of 3 feet is given as a function of time t (in seconds) by s(t) = -16t2 + 70t + 3. What is the maximum height? Round to the Nearest hundredth, if necessary.

Find the value for the function. - f(x+h) when f(x)=−3x+87x−9f ( x + h ) \text { when } f ( x ) = \frac { - 3 x + 8 } { 7 x - 9 }f(x+h) when f(x)=7x−9−3x+8​

The graph of a piecewise-defined function is given. Write a definition for the function. -

Find the function. -Find the function that is finally graphed after the following transformations are applied to the graph of y = |x|. The graph is shifted right 3 units, stretched by a factor of 3, shifted vertically down 2 units, and finally reflected Across the x-axis.

Given the functi is the point (-1, 4) on the graph of f? - f(x)=x2−3x+2f ( x ) = \frac { x ^ { 2 } - 3 } { x + 2 }f(x)=x+2x2−3​

Find and simplify the difference quotient of f f(x+h)−f(x)h\frac { f ( x + h ) - f ( x ) } { h }hf(x+h)−f(x)​ , h ≠ 0, for the function. - f(x)=x2+6x−8f ( x ) = x ^ { 2 } + 6 x - 8f(x)=x2+6x−8

Find the domain of the function. - h(x)=x−1x3−25xh ( x ) = \frac { x - 1 } { x ^ { 3 } - 25 x }h(x)=x3−25xx−1​

Linear and Quadratic Functions

Polynomial and Rational Functions

Conics

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

Filters

Find and simplify the difference quotient of f $\frac { f ( x + h ) - f ( x ) } { h }$ , h ≠ 0, for the function. - $( x ) = \frac { 1 } { 7 x }$

Determine algebraically whether the function is even, odd, or neither. - $f ( x ) = - 2 x ^ { 4 } - x ^ { 2 }$

Determine algebraically whether the function is even, odd, or neither. - $f ( x ) = \frac { 1 } { x ^ { 2 } }$

Answer the question about the given function. -Given the functi $f ( x ) = - 6 x ^ { 2 } + 12 x - 9$ , if x = 1, what is f(x)? What point is on the graph of f?

Find the value for the function. -Find f( $( x + h ) \text { when } f ( x ) = 2 x ^ { 2 } - 2 x - 5$

Solve the problem. -The height s of a ball (in feet) thrown with an initial velocity of 70 feet per second from an initial height of 3 feet is given as a function of time t (in seconds) by s(t) = -16t² + 70t + 3. What is the maximum height? Round to the Nearest hundredth, if necessary.

Find the value for the function. - $f ( x + h ) \text { when } f ( x ) = \frac { - 3 x + 8 } { 7 x - 9 }$

Given the functi is the point (-1, 4) on the graph of f? - $f ( x ) = \frac { x ^ { 2 } - 3 } { x + 2 }$

Find and simplify the difference quotient of f $\frac { f ( x + h ) - f ( x ) } { h }$ , h ≠ 0, for the function. - $f ( x ) = x ^ { 2 } + 6 x - 8$

Find the domain of the function. - $h ( x ) = \frac { x - 1 } { x ^ { 3 } - 25 x }$