Question 1

Find the average rate of change for the function between the given values.
-$f ( x ) = \sqrt { 2 x } ;$ from 2 to 8

Accepted Answer

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

Question 2

Suppose the point (2, 4) is on the graph of y = f(x). Find a point on the graph of the given function.
-$$y = f ( x + 3 )$$

Accepted Answer

A)  $( 2,1 )$
В) $( - 1,4 )$ 
C)  $( 5,4 )$ 
D)  $( 2,7 )$ 
A)  $( 2,1 )$
В) $( - 1,4 )$ 
C)  $( 5,4 )$ 
D)  $( 2,7 )$

Question 3

Determine whether the equation defines y as a function of x.
-$x+7 y=5$

Accepted Answer

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

Question 4

Determine algebraically whether the function is even, odd, or neither.
-$f ( x ) = \frac { - x ^ { 3 } } { 9 x ^ { 2 } + 7 }$

Accepted Answer

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

Question 5

Solve the problem.
-If a rock falls from a height of 80 meters on Earth, the height H (in meters) after x seconds is approximately $$H ( x ) = 80 - 4.9 x ^ { 2 }$$ What is the height of the rock when x = 1.5 seconds? Round to the nearest hundredth, if necessary.

Accepted Answer

A)  72.65 m 
B)  68.98 m 
C)  91.03 m 
D)  69.2 m 
A)  72.65 m 
B)  68.98 m 
C)  91.03 m 
D)  69.2 m

Question 6

Determine algebraically whether the function is even, odd, or neither.
-$f ( x ) = 5 x ^ { 4 } - x ^ { 2 }$

Accepted Answer

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

Question 7

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 8

Use a graphing utility to graph the function over the indicated interval and approximate any local maxima and local
minima. Determine where the function is increasing and where it is decreasing. If necessary, round answers to two
decimal places.
-$$f ( x ) = - 0.3 x ^ { 3 } + 0.2 x ^ { 2 } + 4 x - 5 ; ( - 4,5 )$$

Accepted Answer

local maximum at (2.34, 1.61)

Question 9

Find the average rate of change for the function between the given values.
-$f ( x ) = x ^ { 2 } + 6 x$; from 3 to 7

Accepted Answer

A)  $\frac { 91 } { 4 }$

В) $\frac { 64 } { 7 }$ 
C)  13 
D)  16 
A)  $\frac { 91 } { 4 }$

В) $\frac { 64 } { 7 }$ 
C)  13 
D)  16

Question 10

Solve the problem.
-The amount of time it takes a swimmer to swim a race is inversely proportional to the average speed of the swimmer. A swimmer finishes a race in 30 seconds with an average speed of 5 feet per second. Find the average
Speed of the swimmer if it takes 25 seconds to finish the race.

Accepted Answer

A)  8 feet per second 
B)  7 feet per second 
C)  5 feet per second 
D)  6 feet per second 
A)  8 feet per second 
B)  7 feet per second 
C)  5 feet per second 
D)  6 feet per second

Question 11

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.
-$$f ( x ) = x ^ { 2 } + 2 x - 3 ; ( - 5,5 )$$

Accepted Answer

A)  local maximum at $( 1 , - 4 )$ 
B)  local maximum at $( - 1,4 )$ 
C)  local minimum at $( - 1 , - 4 )$ 
D)  local minimum at $( 1,4 )$ 
A)  local maximum at $( 1 , - 4 )$ 
B)  local maximum at $( - 1,4 )$ 
C)  local minimum at $( - 1 , - 4 )$ 
D)  local minimum at $( 1,4 )$

Question 12

Find the value for the function.
-Find $f ( x - 1 )$ when $f ( x ) = 5 x ^ { 2 } - 3 x + 1$

Accepted Answer

A)  $5 x ^ { 2 } + 2 x + 3$ 
B)  $5 x ^ { 2 } - 13 x + 9$ 
C)  $5 x ^ { 2 } - 13 x + 3$ 
D)  $- 13 x ^ { 2 } + 5 x + 9$ 
A)  $5 x ^ { 2 } + 2 x + 3$ 
B)  $5 x ^ { 2 } - 13 x + 9$ 
C)  $5 x ^ { 2 } - 13 x + 3$ 
D)  $- 13 x ^ { 2 } + 5 x + 9$

Question 13

Solve.
-The time in hours it takes a satellite to complete an orbit around the earth varies directly as the radius of the orbit (from the center of the earth) and inversely as the orbital velocity. If a satellite completes an orbit 890 miles
Above the earth in 17 hours at a velocity of 21,000 mph, how long would it take a satellite to complete an orbit if
It is at 1,700 miles above the earth at a velocity of 25,000 mph? (Use 3960 miles as the radius of the earth.)

Accepted Answer

A)  166.65 hours 
B)  27.28 hours 
C)  16.66 hours 
D)  5.01 hours 
A)  166.65 hours 
B)  27.28 hours 
C)  16.66 hours 
D)  5.01 hours

Question 14

The graph of a piecewise-defined function is given. Write a definition for the function.
-  A)
$f(x)=\left\{\begin{array}{ll}
\frac{3}{4} x+4 & \text { if }-3 \leq x \leq 0 \
\frac{3}{2} x & \text { if } x>0
\end{array}\right.$

Accepted Answer

B) $f(x)=\left\{\begin{array}{ll} \frac{4}{3} x+4 & \text { if }-3 \leq x \leq 0 \ \frac{2}{3} x & \text { if } x>0 \end{array}\right.$ C) $f(x)=\left\{\begin{array}{ll} \frac{3}{4} x+4 & \text { if }-3 \leq x \leq 0 \ \frac{3}{2} x & \text { if } x \geq 0 \end{array}\right.$ D) $f(x)=\left\{\begin{array}{ll} \frac{4}{3} x+4 & \text { if }-3 \leq x \leq 0 \ \frac{2}{3} x & \text { if } 00 \end{array}\right.$ C) $f(x)=\left\{\begin{array}{ll} \frac{3}{4} x+4 & \text { if }-3 \leq x \leq 0 \ \frac{3}{2} x & \text { if } x \geq 0 \end{array}\right.$ D) $f(x)=\left\{\begin{array}{ll} \frac{4}{3} x+4 & \text { if }-3 \leq x \leq 0 \ \frac{2}{3} x & \text { if } 0

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.
-$f(x)=-x^{3}$
 
 A)

Accepted Answer

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

Question 16

Solve.
-The voltage across a resistor is jointly proportional to the resistance of the resistor and the current flowing through the resistor. If the voltage across a resistor is 21 volts for a resistor whose resistance is 3 ohms and when
The current flowing through the resistor is 7 amperes, find the voltage across a resistor whose resistance is
2 ohms and when the current flowing through the resistor is 4 amperes.

Accepted Answer

A)  12 volts 
B)  28 volts 
C)  8 volts 
D)  14 volts 
A)  12 volts 
B)  28 volts 
C)  8 volts 
D)  14 volts

Question 17

Match the correct function to the graph.
-  A) $y = - 2 x ^ { 2 } + 1$

Accepted Answer

B)  $y = - 2 x ^ { 2 } - 1$ 
C)  $y = 1 - x ^ { 2 }$ 
D)  $y = - 2 x ^ { 2 }$ 
B)  $y = - 2 x ^ { 2 } - 1$ 
C)  $y = 1 - x ^ { 2 }$ 
D)  $y = - 2 x ^ { 2 }$

Question 18

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

Accepted Answer

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

Question 19

Find and simplify the difference quotient of f, $$\frac { f ( x + h ) - f ( x ) } { h }$$ $\mathbf { h } \neq 0$ , for the function.
-  A) 
$\begin{array}{l}
\begin{array}{l}
\text { function } \
\text { domain: }\{x \mid x \leq 0\} \
\text { range: }\{y \mid y \geq-2\} \
\text { intercepts: }(-2,0),(0,-2),(2,0)
\end{array}\
\text { symmetry: } y \text {-axis }
\end{array}$

Accepted Answer

B)  
function
domain: $ \{x \mid x \geq-2\} $
range: $ \{y \mid y \leq 0\} $
intercepts: $ (-2,0),(0,-2),(2,0) $
symmetry: none 
C) 
function
domain: all real numbers
range: all real numbers
intercepts: $ (-2,0),(0,-2),(2,0) $
symmetry: none 
D)  not a function 
B)  
function
domain: $ \{x \mid x \geq-2\} $
range: $ \{y \mid y \leq 0\} $
intercepts: $ (-2,0),(0,-2),(2,0) $
symmetry: none 
C) 
function
domain: all real numbers
range: all real numbers
intercepts: $ (-2,0),(0,-2),(2,0) $
symmetry: none 
D)  not a function

Question 20

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

Find the average rate of change for the function between the given values. - $f ( x ) = \sqrt { 2 x } ;$ from 2 to 8

Suppose the point (2, 4) is on the graph of y = f(x). Find a point on the graph of the given function. - $y = f ( x + 3 )$

Determine whether the equation defines y as a function of x. - $x+7 y=5$

Determine algebraically whether the function is even, odd, or neither. - $f ( x ) = \frac { - x ^ { 3 } } { 9 x ^ { 2 } + 7 }$

Solve the problem. -If a rock falls from a height of 80 meters on Earth, the height H (in meters) after x seconds is approximately $H ( x ) = 80 - 4.9 x ^ { 2 }$ What is the height of the rock when x = 1.5 seconds? Round to the nearest hundredth, if necessary.

Determine algebraically whether the function is even, odd, or neither. - $f ( x ) = 5 x ^ { 4 } - x ^ { 2 }$

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 $f$ .

Find the average rate of change for the function between the given values. - $f ( x ) = x ^ { 2 } + 6 x$ ; from 3 to 7

Solve the problem. -The amount of time it takes a swimmer to swim a race is inversely proportional to the average speed of the swimmer. A swimmer finishes a race in 30 seconds with an average speed of 5 feet per second. Find the average Speed of the swimmer if it takes 25 seconds to finish the race.

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. - $f ( x ) = x ^ { 2 } + 2 x - 3 ; ( - 5,5 )$

Find the value for the function. -Find $f ( x - 1 )$ when $f ( x ) = 5 x ^ { 2 } - 3 x + 1$

Match the correct function to the graph. - $Match the correct function to the graph. - A) y = - 2 x ^ { 2 } + 1 B) y = - 2 x ^ { 2 } - 1 C) y = 1 - x ^ { 2 } D) y = - 2 x ^ { 2 }$ A) $y = - 2 x ^ { 2 } + 1$ B) $y = - 2 x ^ { 2 } - 1$ C) $y = 1 - x ^ { 2 }$ D) $y = - 2 x ^ { 2 }$

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?

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

Review

Filters

Exam 1: Functions and Their Graphs

Find the average rate of change for the function between the given values. - f(x)=2x;f ( x ) = \sqrt { 2 x } ;f(x)=2x​; from 2 to 8

Suppose the point (2, 4) is on the graph of y = f(x). Find a point on the graph of the given function. - y=f(x+3)y = f ( x + 3 )y=f(x+3)

Determine whether the equation defines y as a function of x. - x+7y=5x+7 y=5x+7y=5

Determine algebraically whether the function is even, odd, or neither. - f(x)=−x39x2+7f ( x ) = \frac { - x ^ { 3 } } { 9 x ^ { 2 } + 7 }f(x)=9x2+7−x3​

Solve the problem. -If a rock falls from a height of 80 meters on Earth, the height H (in meters) after x seconds is approximately H(x)=80−4.9x2H ( x ) = 80 - 4.9 x ^ { 2 }H(x)=80−4.9x2 What is the height of the rock when x = 1.5 seconds? Round to the nearest hundredth, if necessary.

Determine algebraically whether the function is even, odd, or neither. - f(x)=5x4−x2f ( x ) = 5 x ^ { 4 } - x ^ { 2 }f(x)=5x4−x2

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 .

Find the average rate of change for the function between the given values. - f(x)=x2+6xf ( x ) = x ^ { 2 } + 6 xf(x)=x2+6x ; from 3 to 7

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)=x2+2x−3;(−5,5)f ( x ) = x ^ { 2 } + 2 x - 3 ; ( - 5,5 )f(x)=x2+2x−3;(−5,5)

Find the value for the function. -Find f(x−1)f ( x - 1 )f(x−1) when f(x)=5x2−3x+1f ( x ) = 5 x ^ { 2 } - 3 x + 1f(x)=5x2−3x+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)=−x3f(x)=-x^{3}f(x)=−x3 A) B) C) D)

Match the correct function to the graph. - A) y=−2x2+1y = - 2 x ^ { 2 } + 1y=−2x2+1 B) y=−2x2−1y = - 2 x ^ { 2 } - 1y=−2x2−1 C) y=1−x2y = 1 - x ^ { 2 }y=1−x2 D) y=−2x2y = - 2 x ^ { 2 }y=−2x2

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)=13xf(x)=\frac{1}{3} \sqrt{x}f(x)=31​x​ A) B) C) D)