Question 1

Solve the problem.
-A rectangle that is $x$ feet wide is inscribed in a circle of radius 36 feet. Express the area of the rectangle as a function of $x$.

Accepted Answer

A)  $\mathrm { A } ( \mathrm { x } ) = \mathrm { x } ^ { 2 } \sqrt { 2,592 - \mathrm { x } ^ { 2 } }$ 
B)  $A ( x ) = x \sqrt { 5,184 - x ^ { 2 } }$ 
C)  $\mathrm { A } ( \mathrm { x } ) = \mathrm { x } \left( 5,184 - \mathrm { x } ^ { 2 } \right)$ 
D)  $\mathrm { A } ( \mathrm { x } ) = \mathrm { x } \sqrt { 3,888 - \mathrm { x } }$ 
A)  $\mathrm { A } ( \mathrm { x } ) = \mathrm { x } ^ { 2 } \sqrt { 2,592 - \mathrm { x } ^ { 2 } }$ 
B)  $A ( x ) = x \sqrt { 5,184 - x ^ { 2 } }$ 
C)  $\mathrm { A } ( \mathrm { x } ) = \mathrm { x } \left( 5,184 - \mathrm { x } ^ { 2 } \right)$ 
D)  $\mathrm { A } ( \mathrm { x } ) = \mathrm { x } \sqrt { 3,888 - \mathrm { x } }$

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.
-The reflection of the graph of y = f(x) across the x-axis

Accepted Answer

A)  (2, -4) 
B)  (-2, 4) 
C)  (2, 4) 
D)  (-2, -4) 
A)  (2, -4) 
B)  (-2, 4) 
C)  (2, 4) 
D)  (-2, -4)

Question 3

Find the domain of the function.
-$$h ( x ) = \frac { x - 2 } { x ^ { 3 } - 9 x }$$

Accepted Answer

A)  $\{ x \mid x \neq 2 \}$ 
B)  $\{ x \mid x \neq 0 \}$ 
C)  all real numbers 
D)  $\{ x \mid x \neq - 3,0,3 \}$ 
A)  $\{ x \mid x \neq 2 \}$ 
B)  $\{ x \mid x \neq 0 \}$ 
C)  all real numbers 
D)  $\{ x \mid x \neq - 3,0,3 \}$

Question 4

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.
-$$f ( x ) = x ^ { 4 } - 5 x ^ { 3 } + 3 x ^ { 2 } + 9 x - 3 ; ( - 5,5 )$$

Accepted Answer

A) local minimum at $ (-0.57,-6.12) $
local maximum at $ (1.32,5.64) $
local minimum at $ (3,-3) $ 
B)  local minimum at $ (-1,-6) $
local maximum at $ (1,6) $
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 $( - 3 , - 3 )$
local maximum at $( - 1.32,5.64 )$
local minimum at $( 0.57 , - 6.12 )$ 
A) local minimum at $ (-0.57,-6.12) $
local maximum at $ (1.32,5.64) $
local minimum at $ (3,-3) $ 
B)  local minimum at $ (-1,-6) $
local maximum at $ (1,6) $
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 $( - 3 , - 3 )$
local maximum at $( - 1.32,5.64 )$
local minimum at $( 0.57 , - 6.12 )$

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

Question 6

Determine algebraically whether the function is even, odd, or neither.
-$$f ( x ) = \sqrt [ 3 ] { x }$$

Accepted Answer

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

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.
-$f(x)=(x-5)^{2}$

Accepted Answer

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

Question 8

Graph the function.
-$$f ( x ) = \left\{ \begin{array} { l l } 
x + 1 & \text { if } - 8 \leq x  6
\end{array} \right.$$

Accepted Answer

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

Question 9

Suppose the point (2, 4) is on the graph of y = f(x). Find a point on the graph of the given function.
-The reflection of the graph of y = f(x) across the y-axis

Accepted Answer

A)  (-2, -4) 
B)  (2, -4) 
C)  (-2, 4) 
D)  (2, 4) 
A)  (-2, -4) 
B)  (2, -4) 
C)  (-2, 4) 
D)  (2, 4)

Question 10

Solve the problem.
-If the force acting on an object stays the same, then the acceleration of the object is inversely proportional to its mass. If an object with a mass of 21 kilograms accelerates at a rate of 9 meters per second per second by a force,
Find the rate of acceleration of an object with a mass of 7 kilograms that is pulled by the same force.

Accepted Answer

A)  18 meters per second per second 
B)  24 meters per second per second 
C)  3 meters per second per second 
D)  27 meters per second per second 
A)  18 meters per second per second 
B)  24 meters per second per second 
C)  3 meters per second per second 
D)  27 meters per second per second

Question 11

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 12

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 13

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given
interval.
-$$( - 2.5,2.2 )$$

Accepted Answer

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

Question 14

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 15

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given
interval.
-$$( 1 , \infty )$$

Accepted Answer

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

Question 16

Solve the problem.
-Elissa wants to set up a rectangular dog run in her backyard. She has 24 feet of fencing to work with and wants to use it all. If the dog run is to be $x$ feet long, express the area of the dog run as a function of $x$.

Accepted Answer

A)  $A ( x ) = 11 x - x ^ { 2 }$ 
B)  $\mathrm { A } ( \mathrm { x } ) = 13 \mathrm { x } - \mathrm { x } ^ { 2 }$ 
C)  $\mathrm { A } ( \mathrm { x } ) = 14 \mathrm { x } ^ { 2 } - \mathrm { x }$ 
D)  $A ( x ) = 12 x - x ^ { 2 }$ 
A)  $A ( x ) = 11 x - x ^ { 2 }$ 
B)  $\mathrm { A } ( \mathrm { x } ) = 13 \mathrm { x } - \mathrm { x } ^ { 2 }$ 
C)  $\mathrm { A } ( \mathrm { x } ) = 14 \mathrm { x } ^ { 2 } - \mathrm { x }$ 
D)  $A ( x ) = 12 x - x ^ { 2 }$

Question 17

The graph of a function f is given. Use the graph to answer the question.
-What are the $x$-intercepts?

Accepted Answer

A)  $- 10 , - 6,7,10$ 
B)  $- 6,7$ 
C)  $- 6,7,10$ 
D)  $- 6$ 
A)  $- 10 , - 6,7,10$ 
B)  $- 6,7$ 
C)  $- 6,7,10$ 
D)  $- 6$

Question 18

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

Accepted Answer

A)  Decreasing on $( - 3 , - 1 )$ and $( 1,4 )$; increasing on $( - 2,1 )$ 
B)  Increasing on $( - 3 , - 2 )$ and $( 2,4 )$; decreasing on $( - 1,1 )$; constant on $( - 2 , - 1 )$ and $( 1,2 )$ 
C)  Decreasing on $( - 3 , - 2 )$ and $( 2,4 )$; increasing on $( - 1,1 )$ 
D)  Decreasing on $( - 3 , - 2 )$ and $( 2,4 )$; increasing on $( - 1,1 )$; constant on $( - 2 , - 1 )$ and $( 1,2 )$ 
A)  Decreasing on $( - 3 , - 1 )$ and $( 1,4 )$; increasing on $( - 2,1 )$ 
B)  Increasing on $( - 3 , - 2 )$ and $( 2,4 )$; decreasing on $( - 1,1 )$; constant on $( - 2 , - 1 )$ and $( 1,2 )$ 
C)  Decreasing on $( - 3 , - 2 )$ and $( 2,4 )$; increasing on $( - 1,1 )$ 
D)  Decreasing on $( - 3 , - 2 )$ and $( 2,4 )$; increasing on $( - 1,1 )$; constant on $( - 2 , - 1 )$ and $( 1,2 )$

Question 19

Graph the function.
-$$f ( x ) = \frac { 1 } { x }$$

Accepted Answer

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

Question 20

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 down 4 units, reflected about the $y$-axis, and finally shifted left 6 units.

Accepted Answer

A)  $y = | - x - 6 | + 4$ 
B)  $y = - | x + 6 | - 4$ 
C)  $y = | - x - 6 | - 4$ 
D)  $y = | - x + 6 | + 4$ 
A)  $y = | - x - 6 | + 4$ 
B)  $y = - | x + 6 | - 4$ 
C)  $y = | - x - 6 | - 4$ 
D)  $y = | - x + 6 | + 4$

Solve the problem. -A rectangle that is $x$ feet wide is inscribed in a circle of radius 36 feet. Express the area of the rectangle as a function of $x$ .

Suppose the point (2, 4) is on the graph of y = f(x). Find a point on the graph of the given function. -The reflection of the graph of y = f(x) across the x-axis

Find the domain of the function. - $h ( x ) = \frac { x - 2 } { x ^ { 3 } - 9 x }$

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. - $f ( x ) = \sqrt [ 3 ] { x }$

Suppose the point (2, 4) is on the graph of y = f(x). Find a point on the graph of the given function. -The reflection of the graph of y = f(x) across the y-axis

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

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

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. - $( - 2.5,2.2 )$

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. - $( 1 , \infty )$ $The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. - ( 1 , \infty )$

Solve the problem. -Elissa wants to set up a rectangular dog run in her backyard. She has 24 feet of fencing to work with and wants to use it all. If the dog run is to be $x$ feet long, express the area of the dog run as a function of $x$ .

The graph of a function f is given. Use the graph to answer the question. -What are the $x$ -intercepts?

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

Graph the function. - $f ( x ) = \frac { 1 } { x }$ $Graph the function. - f ( x ) = \frac { 1 } { x }$

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 down 4 units, reflected about the $y$ -axis, and finally shifted left 6 units.

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

Solve the problem. -A rectangle that is xxx feet wide is inscribed in a circle of radius 36 feet. Express the area of the rectangle as a function of xxx .

Suppose the point (2, 4) is on the graph of y = f(x). Find a point on the graph of the given function. -The reflection of the graph of y = f(x) across the x-axis

Find the domain of the function. - h(x)=x−2x3−9xh ( x ) = \frac { x - 2 } { x ^ { 3 } - 9 x }h(x)=x3−9xx−2​

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

Determine algebraically whether the function is even, odd, or neither. - f(x)=x3f ( x ) = \sqrt [ 3 ] { x }f(x)=3x​

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−5)2f(x)=(x-5)^{2}f(x)=(x−5)2

Graph the function. - f(x)={x+1 if −8≤x<6−5 if x=6−x+10 if x>6f ( x ) = \left\{ \begin{array} { l l } x + 1 & \text { if } - 8 \leq x < 6 \\- 5 & \text { if } x = 6 \\- x + 10 & \text { if } x > 6\end{array} \right.f(x)=⎩⎨⎧​x+1−5−x+10​ if −8≤x<6 if x=6 if x>6​

Suppose the point (2, 4) is on the graph of y = f(x). Find a point on the graph of the given function. -The reflection of the graph of y = f(x) across the y-axis

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

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

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. - (−2.5,2.2)( - 2.5,2.2 )(−2.5,2.2)

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. - (1,∞)( 1 , \infty )(1,∞)

Solve the problem. -Elissa wants to set up a rectangular dog run in her backyard. She has 24 feet of fencing to work with and wants to use it all. If the dog run is to be xxx feet long, express the area of the dog run as a function of xxx .

The graph of a function f is given. Use the graph to answer the question. -What are the xxx -intercepts?

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

Graph the function. - f(x)=1xf ( x ) = \frac { 1 } { x }f(x)=x1​

Find the function. -Find the function that is finally graphed after the following transformations are applied to the graph of y=∣x∣y = | x |y=∣x∣ . The graph is shifted down 4 units, reflected about the yyy -axis, and finally shifted left 6 units.

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

Solve the problem. -A rectangle that is $x$ feet wide is inscribed in a circle of radius 36 feet. Express the area of the rectangle as a function of $x$ .

Find the domain of the function. - $h ( x ) = \frac { x - 2 } { x ^ { 3 } - 9 x }$

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. - $f ( x ) = \sqrt [ 3 ] { x }$

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

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. - $( - 2.5,2.2 )$

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. - $( 1 , \infty )$ $The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. - ( 1 , \infty )$

Solve the problem. -Elissa wants to set up a rectangular dog run in her backyard. She has 24 feet of fencing to work with and wants to use it all. If the dog run is to be $x$ feet long, express the area of the dog run as a function of $x$ .

The graph of a function f is given. Use the graph to answer the question. -What are the $x$ -intercepts?

Graph the function. - $f ( x ) = \frac { 1 } { x }$ $Graph the function. - f ( x ) = \frac { 1 } { x }$

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 down 4 units, reflected about the $y$ -axis, and finally shifted left 6 units.