Question 1

Match the equation to the correct graph.
-$$y = ( x - 7 ) ^ { 2 }$$

Accepted Answer

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

Question 2

Solve the problem.
-If m varies directly as p, and m = 63 when p = 9, find m when p is 3.

Accepted Answer

A)  9 
B)  21 
C)  81 
D)  49 
A)  9 
B)  21 
C)  81 
D)  49

Question 3

Solve the problem.
-As one approaches a certain sound source, the sound intensity in arbitrary units increases according to the following function of time: $F ( x ) = - \frac { 2 ( x - 6 ) ^ { 2 } + 5 ( x - 6 ) - 4 } { 2 ( x - 6 ) + 60 }$. Starting at $x = 0$, when the source of sound is first sensed, how much time elapses until maximum sound intensity is felt? Round the result to the nearest hundredth.

Accepted Answer

A)  $0.12 \mathrm { sec }$ 
B)  $52.69 \mathrm { sec }$ 
C)  $4.69 \mathrm { sec }$ 
D)  $29.92 \mathrm { sec }$ 
A)  $0.12 \mathrm { sec }$ 
B)  $52.69 \mathrm { sec }$ 
C)  $4.69 \mathrm { sec }$ 
D)  $29.92 \mathrm { sec }$

Question 4

Use Descartesʹ Rule of Signs to determine the possible number of positive real zeros and the possible negative real zeros for the function.
-$$- 4 x ^ { 4 } + 3 x ^ { 3 } - 7 x ^ { 2 } + 6 x - 9 = 0$$

Accepted Answer

A)  Positive $( 2,0 )$, negative $( 4,2,0 )$ 
B)  Positive $( 2,0 )$, negative $( 2,0 )$ 
C)  Positive $( 4,2,0 )$, negative $( 0 )$ 
D)  Positive $( 4,2,0 )$, negative $( 4,2,0 )$ 
A)  Positive $( 2,0 )$, negative $( 4,2,0 )$ 
B)  Positive $( 2,0 )$, negative $( 2,0 )$ 
C)  Positive $( 4,2,0 )$, negative $( 0 )$ 
D)  Positive $( 4,2,0 )$, negative $( 4,2,0 )$

Question 5

Give the domain and range for the rational function. Use interval notation.
-$$f ( x ) = \frac { 2 } { x } + 3$$

Accepted Answer

A)  Domain: $( - \infty , 3 ) \cup ( 3 , \infty ) ;$ Range: $( - \infty , 0 ) \cup ( 0 , \infty )$ 
B)  Domain: $( - \infty , 0 ) \cup ( 0 , \infty )$; Range: $( - \infty , - 3 ) \cup ( - 3 , \infty )$ 
C)  Domain: $( - \infty , 2 ) \cup ( 2 , \infty )$; Range: $( - \infty , 3 ) \cup ( 3 , \infty )$ 
D)  Domain: $( - \infty , 0 ) \cup ( 0 , \infty ) ;$ Range: $( - \infty , 3 ) \cup ( 3 , \infty )$ 
A)  Domain: $( - \infty , 3 ) \cup ( 3 , \infty ) ;$ Range: $( - \infty , 0 ) \cup ( 0 , \infty )$ 
B)  Domain: $( - \infty , 0 ) \cup ( 0 , \infty )$; Range: $( - \infty , - 3 ) \cup ( - 3 , \infty )$ 
C)  Domain: $( - \infty , 2 ) \cup ( 2 , \infty )$; Range: $( - \infty , 3 ) \cup ( 3 , \infty )$ 
D)  Domain: $( - \infty , 0 ) \cup ( 0 , \infty ) ;$ Range: $( - \infty , 3 ) \cup ( 3 , \infty )$

Question 6

Solve the problem.
-A rectangular piece of cardboard measuring 30 inches by 50 inches is to be made into a box with an open top by cutting equal size squares from each corner and folding up the sides. Let $x$ represent the length of a side of each such square. For what value of $x$ will the volume be a maximum? If necessary, round to 2 decimal places.

Accepted Answer

A)  $20.6$ in. 
B)  $6.07 \mathrm { in }$. 
C)  $25 \mathrm { in }$. 
D)  $41.2$ in. 
A)  $20.6$ in. 
B)  $6.07 \mathrm { in }$. 
C)  $25 \mathrm { in }$. 
D)  $41.2$ in.

Question 7

Solve the problem. Round to the nearest tenth unless indicated otherwise.
-The force needed to keep a car from skidding on a curve varies jointly as the weight of the car and the square of the carʹs speed, and inversely as the radius of the curve. If a force of 3600 pounds is
Needed to keep an 1800 pound car traveling at 20 mph from skidding on a curve of radius 600 feet,
What force would be required to keep the same car from skidding on a curve of radius 660 feet at
40 mph? Round your answer to the nearest pound of force.

Accepted Answer

A)  12,959 lb 
B)  13,123 lb 
C)  13,091 lb 
D)  13,661 lb 
A)  12,959 lb 
B)  13,123 lb 
C)  13,091 lb 
D)  13,661 lb

Question 8

Find an equation for the rational function graph.
-

Accepted Answer

A)  $f ( x ) = \frac { 2 ( x + 4 ) ( x + 6 ) } { ( x + 3 ) ( x + 6 ) }$ 
B)  $f ( x ) = \frac { 2 ( x - 4 ) } { x - 3 }$ 
C)  $f ( x ) = \frac { 2 ( x - 3 ) ( x - 6 ) } { ( x - 4 ) ( x - 6 ) }$ 
D)  $f ( x ) = \frac { 2 ( x - 4 ) ( x - 6 ) } { ( x - 3 ) ( x - 6 ) }$ 
A)  $f ( x ) = \frac { 2 ( x + 4 ) ( x + 6 ) } { ( x + 3 ) ( x + 6 ) }$ 
B)  $f ( x ) = \frac { 2 ( x - 4 ) } { x - 3 }$ 
C)  $f ( x ) = \frac { 2 ( x - 3 ) ( x - 6 ) } { ( x - 4 ) ( x - 6 ) }$ 
D)  $f ( x ) = \frac { 2 ( x - 4 ) ( x - 6 ) } { ( x - 3 ) ( x - 6 ) }$

Question 9

Solve the inequality. Write the solution set in interval notation.
-$$- x ^ { 2 } + 8 x - 13 \geq 0$$

Accepted Answer

A)  $[ - 4 - \sqrt { 3 } , - 4 + \sqrt { 3 } ]$ 
B)  $( - \infty , 4 - \sqrt { 3 } ] \cup [ 4 + \sqrt { 3 } , \infty )$ 
C)  $( - \infty , - 4 - \sqrt { 3 } ] \cup [ - 4 + \sqrt { 3 } , \infty )$ 
D)  $[ 4 - \sqrt { 3 } , 4 + \sqrt { 3 } ]$ 
A)  $[ - 4 - \sqrt { 3 } , - 4 + \sqrt { 3 } ]$ 
B)  $( - \infty , 4 - \sqrt { 3 } ] \cup [ 4 + \sqrt { 3 } , \infty )$ 
C)  $( - \infty , - 4 - \sqrt { 3 } ] \cup [ - 4 + \sqrt { 3 } , \infty )$ 
D)  $[ 4 - \sqrt { 3 } , 4 + \sqrt { 3 } ]$

Question 10

Determine which of the rational functions given below has the following feature(s).
-x-intercepts: 2 and $5 , y$-intercept: 10 , vertical asymptote: $x = 1$, horizontal asymptote: $y = 1$

Accepted Answer

A)  $f ( x ) = \frac { ( x - 2 ) ( x - 5 ) } { ( x - 1 ) }$ 
B)  $f ( x ) = \frac { ( x - 2 ) ( x - 5 ) } { ( x - 1 ) ^ { 2 } }$ 
C)  $f ( x ) = \frac { ( x + 2 ) ( x + 5 ) } { ( x + 1 ) }$ 
D)  $f ( x ) = \frac { ( x + 2 ) ( x + 5 ) } { ( x + 1 ) ^ { 2 } }$ 
A)  $f ( x ) = \frac { ( x - 2 ) ( x - 5 ) } { ( x - 1 ) }$ 
B)  $f ( x ) = \frac { ( x - 2 ) ( x - 5 ) } { ( x - 1 ) ^ { 2 } }$ 
C)  $f ( x ) = \frac { ( x + 2 ) ( x + 5 ) } { ( x + 1 ) }$ 
D)  $f ( x ) = \frac { ( x + 2 ) ( x + 5 ) } { ( x + 1 ) ^ { 2 } }$

Question 11

Use the intermediate value theorem for polynomials to show that the polynomial function has a real zero between the
numbers given.
-$f ( x ) = 7 x ^ { 4 } - 8 x ^ { 2 } - 1 ; 1$ and 2

Accepted Answer

A)  $f ( 1 ) = - 2$ and $f ( 2 ) = 79$ 
B)  $f ( 1 ) = 2$ and $f ( 2 ) = 79$ 
C)  $f ( 1 ) = 2$ and $f ( 2 ) = - 79$ 
D)  $f ( 1 ) = - 1$ and $f ( 2 ) = 80$ 
A)  $f ( 1 ) = - 2$ and $f ( 2 ) = 79$ 
B)  $f ( 1 ) = 2$ and $f ( 2 ) = 79$ 
C)  $f ( 1 ) = 2$ and $f ( 2 ) = - 79$ 
D)  $f ( 1 ) = - 1$ and $f ( 2 ) = 80$

Question 12

Express f(x) in the form f(x) = (x - k)q(x) + r for the given value of k.
-$$f ( x ) = 3 x ^ { 3 } - x ^ { 2 } + 2 x + 4 ; k = - 1$$

Accepted Answer

A)  $f ( x ) = ( x + 1 ) \left( 3 x ^ { 2 } - 4 x + 2 \right) + 6$ 
B)  $f ( x ) = ( x + 1 ) \left( 3 x ^ { 2 } - 4 x + 6 \right) - 2$ 
C)  $f ( x ) = ( x - 1 ) \left( 3 x ^ { 2 } + 2 x \right) + 4$ 
D)  $f ( x ) = ( x + 1 ) \left( 3 x ^ { 2 } + 2 x \right) + 4$ 
A)  $f ( x ) = ( x + 1 ) \left( 3 x ^ { 2 } - 4 x + 2 \right) + 6$ 
B)  $f ( x ) = ( x + 1 ) \left( 3 x ^ { 2 } - 4 x + 6 \right) - 2$ 
C)  $f ( x ) = ( x - 1 ) \left( 3 x ^ { 2 } + 2 x \right) + 4$ 
D)  $f ( x ) = ( x + 1 ) \left( 3 x ^ { 2 } + 2 x \right) + 4$

Question 13

Sketch the graph of the rational function.
-$$f ( x ) = \frac { x ( x - 5 ) } { ( x + 4 ) ^ { 2 } }$$

Accepted Answer

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

Question 14

Match the equation to the correct graph.
-$$y = x ^ { 2 } - 6$$

Accepted Answer

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

Question 15

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary.
-$$f ( x ) = x ^ { 3 } - 8 x ^ { 2 } + 17 x - 30$$

Accepted Answer

A)  $6,1 + \sqrt { 5 } , 1 - \sqrt { 5 }$ 
B)  $6 , - 1 + 2 i , - 1 - 2 i$ 
C)  $6,1 + 2 i , 1 - 2 i$ 
D)  $6,1 + \sqrt { 5 } i , 1 - \sqrt { 5 } i$ 
A)  $6,1 + \sqrt { 5 } , 1 - \sqrt { 5 }$ 
B)  $6 , - 1 + 2 i , - 1 - 2 i$ 
C)  $6,1 + 2 i , 1 - 2 i$ 
D)  $6,1 + \sqrt { 5 } i , 1 - \sqrt { 5 } i$

Question 16

Solve.
-The average cost for an adult funeral in Oak City has increased as shown in the table below:

Use a linear function to estimate the cost of an adult funeral in year 20 and 30 .

Accepted Answer

A)  $\$ 5340 ; \$ 6000$ 
B)  $\$ 5000$; $\$ 5340$ 
C)  $\$ 4800 ; \$ 5170$ 
D)  $\$ 5000 ; \$ 6700$ 
A)  $\$ 5340 ; \$ 6000$ 
B)  $\$ 5000$; $\$ 5340$ 
C)  $\$ 4800 ; \$ 5170$ 
D)  $\$ 5000 ; \$ 6700$

Question 17

Determine whether the statement is true or false.
-$$\text { The function } \mathrm { f } ( \mathrm { x } ) = \frac { 1 } { \mathrm { x } } \text { is decreasing on the interval } ( - \infty , \infty )$$

Accepted Answer

A) True 
 B)False

Question 18

Solve the problem.
-A furniture manufacturer decides to make a new line of desks. The table shows the profit, in thousands of dollars, for various levels of production.

Find a quadratic function to model the data, and use the model to predict the profit if 450 chairs are made. Round to the nearest thousand.

Accepted Answer

A)  $\$ 45,000$ 
B)  $\$ 42,000$ 
C)  $\$ 40,000$ 
D)  $\$ 44,000$ 
A)  $\$ 45,000$ 
B)  $\$ 42,000$ 
C)  $\$ 40,000$ 
D)  $\$ 44,000$

Question 19

Provide an appropriate response.
-For what value of $c$ does the quadratic function $f ( x ) = x ^ { 2 } - 6 x + c$ have exactly one $x$-intercept?

Accepted Answer

A)  $- 9$ 
B)  24 
C)  9 
D)  $\frac { 3 } { 2 }$ 
A)  $- 9$ 
B)  24 
C)  9 
D)  $\frac { 3 } { 2 }$

Question 20

Solve the problem.
-$f(x)=(x+3)^{2}$

Accepted Answer

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

Match the equation to the correct graph. - $y = ( x - 7 ) ^ { 2 }$

Solve the problem. -If m varies directly as p, and m = 63 when p = 9, find m when p is 3.

Use Descartesʹ Rule of Signs to determine the possible number of positive real zeros and the possible negative real zeros for the function. - $- 4 x ^ { 4 } + 3 x ^ { 3 } - 7 x ^ { 2 } + 6 x - 9 = 0$

Give the domain and range for the rational function. Use interval notation. - $f ( x ) = \frac { 2 } { x } + 3$

Find an equation for the rational function graph. -

Solve the inequality. Write the solution set in interval notation. - $- x ^ { 2 } + 8 x - 13 \geq 0$

Determine which of the rational functions given below has the following feature(s). -x-intercepts: 2 and $5 , y$ -intercept: 10 , vertical asymptote: $x = 1$ , horizontal asymptote: $y = 1$

Use the intermediate value theorem for polynomials to show that the polynomial function has a real zero between the numbers given. - $f ( x ) = 7 x ^ { 4 } - 8 x ^ { 2 } - 1 ; 1$ and 2

Express f(x) in the form f(x) = (x - k)q(x) + r for the given value of k. - $f ( x ) = 3 x ^ { 3 } - x ^ { 2 } + 2 x + 4 ; k = - 1$

Sketch the graph of the rational function. - $f ( x ) = \frac { x ( x - 5 ) } { ( x + 4 ) ^ { 2 } }$ $Sketch the graph of the rational function. - f ( x ) = \frac { x ( x - 5 ) } { ( x + 4 ) ^ { 2 } }$

Match the equation to the correct graph. - $y = x ^ { 2 } - 6$

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary. - $f ( x ) = x ^ { 3 } - 8 x ^ { 2 } + 17 x - 30$

Solve. -The average cost for an adult funeral in Oak City has increased as shown in the table below: Use a linear function to estimate the cost of an adult funeral in year 20 and 30 .

Determine whether the statement is true or false. - $\text { The function } \mathrm { f } ( \mathrm { x } ) = \frac { 1 } { \mathrm { x } } \text { is decreasing on the interval } ( - \infty , \infty )$

Provide an appropriate response. -For what value of $c$ does the quadratic function $f ( x ) = x ^ { 2 } - 6 x + c$ have exactly one $x$ -intercept?

Solve the problem. - $f(x)=(x+3)^{2}$ $Solve the problem. - f(x)=(x+3)^{2}$

Equations and Inequalities

Graphs and Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Review of Basic Concepts

Filters

Exam 3: Polynomial and Rational Functions

Match the equation to the correct graph. - y=(x−7)2y = ( x - 7 ) ^ { 2 }y=(x−7)2

Solve the problem. -If m varies directly as p, and m = 63 when p = 9, find m when p is 3.

Use Descartesʹ Rule of Signs to determine the possible number of positive real zeros and the possible negative real zeros for the function. - −4x4+3x3−7x2+6x−9=0- 4 x ^ { 4 } + 3 x ^ { 3 } - 7 x ^ { 2 } + 6 x - 9 = 0−4x4+3x3−7x2+6x−9=0

Give the domain and range for the rational function. Use interval notation. - f(x)=2x+3f ( x ) = \frac { 2 } { x } + 3f(x)=x2​+3

Find an equation for the rational function graph. -

Solve the inequality. Write the solution set in interval notation. - −x2+8x−13≥0- x ^ { 2 } + 8 x - 13 \geq 0−x2+8x−13≥0

Determine which of the rational functions given below has the following feature(s). -x-intercepts: 2 and 5,y5 , y5,y -intercept: 10 , vertical asymptote: x=1x = 1x=1 , horizontal asymptote: y=1y = 1y=1

Use the intermediate value theorem for polynomials to show that the polynomial function has a real zero between the numbers given. - f(x)=7x4−8x2−1;1f ( x ) = 7 x ^ { 4 } - 8 x ^ { 2 } - 1 ; 1f(x)=7x4−8x2−1;1 and 2

Express f(x) in the form f(x) = (x - k)q(x) + r for the given value of k. - f(x)=3x3−x2+2x+4;k=−1f ( x ) = 3 x ^ { 3 } - x ^ { 2 } + 2 x + 4 ; k = - 1f(x)=3x3−x2+2x+4;k=−1

Sketch the graph of the rational function. - f(x)=x(x−5)(x+4)2f ( x ) = \frac { x ( x - 5 ) } { ( x + 4 ) ^ { 2 } }f(x)=(x+4)2x(x−5)​

Match the equation to the correct graph. - y=x2−6y = x ^ { 2 } - 6y=x2−6

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary. - f(x)=x3−8x2+17x−30f ( x ) = x ^ { 3 } - 8 x ^ { 2 } + 17 x - 30f(x)=x3−8x2+17x−30

Solve. -The average cost for an adult funeral in Oak City has increased as shown in the table below: Use a linear function to estimate the cost of an adult funeral in year 20 and 30 .

Provide an appropriate response. -For what value of ccc does the quadratic function f(x)=x2−6x+cf ( x ) = x ^ { 2 } - 6 x + cf(x)=x2−6x+c have exactly one xxx -intercept?

Solve the problem. - f(x)=(x+3)2f(x)=(x+3)^{2}f(x)=(x+3)2

Equations and Inequalities

Graphs and Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Review of Basic Concepts

Filters

Match the equation to the correct graph. - $y = ( x - 7 ) ^ { 2 }$

Use Descartesʹ Rule of Signs to determine the possible number of positive real zeros and the possible negative real zeros for the function. - $- 4 x ^ { 4 } + 3 x ^ { 3 } - 7 x ^ { 2 } + 6 x - 9 = 0$

Give the domain and range for the rational function. Use interval notation. - $f ( x ) = \frac { 2 } { x } + 3$

Solve the inequality. Write the solution set in interval notation. - $- x ^ { 2 } + 8 x - 13 \geq 0$

Determine which of the rational functions given below has the following feature(s). -x-intercepts: 2 and $5 , y$ -intercept: 10 , vertical asymptote: $x = 1$ , horizontal asymptote: $y = 1$

Use the intermediate value theorem for polynomials to show that the polynomial function has a real zero between the numbers given. - $f ( x ) = 7 x ^ { 4 } - 8 x ^ { 2 } - 1 ; 1$ and 2

Express f(x) in the form f(x) = (x - k)q(x) + r for the given value of k. - $f ( x ) = 3 x ^ { 3 } - x ^ { 2 } + 2 x + 4 ; k = - 1$

Sketch the graph of the rational function. - $f ( x ) = \frac { x ( x - 5 ) } { ( x + 4 ) ^ { 2 } }$ $Sketch the graph of the rational function. - f ( x ) = \frac { x ( x - 5 ) } { ( x + 4 ) ^ { 2 } }$

Match the equation to the correct graph. - $y = x ^ { 2 } - 6$

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary. - $f ( x ) = x ^ { 3 } - 8 x ^ { 2 } + 17 x - 30$

Provide an appropriate response. -For what value of $c$ does the quadratic function $f ( x ) = x ^ { 2 } - 6 x + c$ have exactly one $x$ -intercept?

Solve the problem. - $f(x)=(x+3)^{2}$ $Solve the problem. - f(x)=(x+3)^{2}$