Question 1

Find the equation that the given graph represents.
-$$f ( x ) = x ^ { 3 } + 2$$

Accepted Answer

A) 
  
B)

C) 
  
D) 
  
A) 
  
B)

C) 
  
D)

Question 2

Give all possible rational zeros for the following polynomial.
-$$P ( x ) = 22 x ^ { 3 } + 88 x ^ { 2 } + 2 x - 11$$

Accepted Answer

A)  $\pm 1 , \pm 11 , \pm \frac { 1 } { 2 }$ 
B)  $\pm 1 , \pm \frac { 1 } { 2 } , \pm 11 , \pm \frac { 11 } { 2 } , \pm \frac { 1 } { 11 } , \pm \frac { 1 } { 22 }$ 
C)  $\pm 1 , \pm \frac { 1 } { 11 } , \pm 2 , \pm \frac { 2 } { 11 } , \pm 11 , \pm 22$ 
D)  $\pm 1 , \pm \frac { 1 } { 2 } , \pm 11 , \pm \frac { 2 } { 11 } , \pm \frac { 1 } { 22 }$ 
A)  $\pm 1 , \pm 11 , \pm \frac { 1 } { 2 }$ 
B)  $\pm 1 , \pm \frac { 1 } { 2 } , \pm 11 , \pm \frac { 11 } { 2 } , \pm \frac { 1 } { 11 } , \pm \frac { 1 } { 22 }$ 
C)  $\pm 1 , \pm \frac { 1 } { 11 } , \pm 2 , \pm \frac { 2 } { 11 } , \pm 11 , \pm 22$ 
D)  $\pm 1 , \pm \frac { 1 } { 2 } , \pm 11 , \pm \frac { 2 } { 11 } , \pm \frac { 1 } { 22 }$

Question 3

Use the intermediate value theorem for polynomials to show that the polynomial function has a real zero between the
numbers given.
-$$f ( x ) = 6 x ^ { 3 } - 10 x + 7 ; - 2 \text { and } - 1$$

Accepted Answer

A)  $f ( - 2 ) = - 21$ and $f ( - 1 ) = 11$ 
B)  $f ( - 2 ) = - 20$ and $f ( - 1 ) = 12$ 
C)  $f ( - 2 ) = 21$ and $f ( - 1 ) = - 11$ 
D)  $f ( - 2 ) = 21$ and $f ( - 1 ) = 11$ 
A)  $f ( - 2 ) = - 21$ and $f ( - 1 ) = 11$ 
B)  $f ( - 2 ) = - 20$ and $f ( - 1 ) = 12$ 
C)  $f ( - 2 ) = 21$ and $f ( - 1 ) = - 11$ 
D)  $f ( - 2 ) = 21$ and $f ( - 1 ) = 11$

Question 4

Use the graph to answer the question.
-Find the domain of the rational function graphed below.   An

Accepted Answer

A)  $( - \infty , - 2 ) \cup ( 2 , \infty )$ 
B)  $( - \infty , 4 ) \cup ( 4 , \infty )$ 
C)  $( - \infty , - 2 ) \cup ( - 2 , \infty )$ 
D)  $( - \infty , - 2 ) \cup ( - 2,2 ) \cup ( 2 , \infty )$ swer: D Determine which of the rational functions given below has the following feature(s). 
A)  $( - \infty , - 2 ) \cup ( 2 , \infty )$ 
B)  $( - \infty , 4 ) \cup ( 4 , \infty )$ 
C)  $( - \infty , - 2 ) \cup ( - 2 , \infty )$ 
D)  $( - \infty , - 2 ) \cup ( - 2,2 ) \cup ( 2 , \infty )$ swer: D Determine which of the rational functions given below has the following feature(s).

Question 5

Match the equation to the correct graph.
-$$y = 2 ( x - 1 ) ^ { 2 } - 2$$

Accepted Answer

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

Question 6

Provide an appropriate response.
-For what values of a does the quadratic function $f ( x ) = a x ^ { 2 } + 4 x + 5$ have two $x$-intercepts?

Accepted Answer

A)  $a  \frac { 16 } { 5 }$ 
C)  $a  \frac { 4 } { 5 }$ 
A)  $a  \frac { 16 } { 5 }$ 
C)  $a  \frac { 4 } { 5 }$

Question 7

Identify the vertex of the parabola.
-$$f ( x ) = ( x - 4 ) ^ { 2 }$$

Accepted Answer

A)  $( 0 , - 4 )$ 
B)  $( - 4,0 )$ 
C)  $( 0,4 )$ 
D)  $( 4,0 )$ 
A)  $( 0 , - 4 )$ 
B)  $( - 4,0 )$ 
C)  $( 0,4 )$ 
D)  $( 4,0 )$

Question 8

Use the factor theorem to decide whether or not the second polynomial is a factor of the first.
-$x ^ { 3 } - 3 x ^ { 2 } + 7 x - 5 ; x - 1$

Accepted Answer

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

Question 9

Use the boundedness theorem to determine whether the polynomial function satisfies the given condition.
-The polynomial $f ( x ) = x ^ { 4 } - x ^ { 3 } + 2 x ^ { 2 } - 4 x - 10$ has no real zero greater than 3 .

Accepted Answer

A)  Yes, the boundedness theorem shows that the polynomial has no real zero greater than 3 . 
B)  No, the boundedness theorem does not show that the polynomial has no real zero greater than 3. 
A)  Yes, the boundedness theorem shows that the polynomial has no real zero greater than 3 . 
B)  No, the boundedness theorem does not show that the polynomial has no real zero greater than 3.

Question 10

Find an equation for the rational function graph.
-

Accepted Answer

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

Question 11

Use the equation and the corresponding graph for the quadratic function to find what is requested.
-$$f ( x ) = ( x - 3 ) ^ { 2 } - 2$$
 
 Find the coordinates of the vertex.

Accepted Answer

A)  (-3, 2) 
B)  (3, -2) 
C)  (-3, -2) 
D)  (3, 0) 
A)  (-3, 2) 
B)  (3, -2) 
C)  (-3, -2) 
D)  (3, 0)

Question 12

Find an equation for the rational function graph.
-

Accepted Answer

A)  $f ( x ) = \frac { x ( x + 6 ) } { x + 7 }$ 
B)  $f ( x ) = \frac { x ( x + 7 ) } { x + 6 }$ 
C)  $f ( x ) = \frac { x + 6 } { x ( x + 7 ) }$ 
D)  $f ( x ) = \frac { x + 7 } { x ( x + 6 ) }$ 
A)  $f ( x ) = \frac { x ( x + 6 ) } { x + 7 }$ 
B)  $f ( x ) = \frac { x ( x + 7 ) } { x + 6 }$ 
C)  $f ( x ) = \frac { x + 6 } { x ( x + 7 ) }$ 
D)  $f ( x ) = \frac { x + 7 } { x ( x + 6 ) }$

Question 13

Use the equation and the corresponding graph for the quadratic function to find what is requested.
-$f(x)=(x-5)^{2}-2$
 
 Find the equation of the axis.

Accepted Answer

A)  y = 2 
B)  x = 5 
C)  x = -5 
D)  y = -2 
A)  y = 2 
B)  x = 5 
C)  x = -5 
D)  y = -2

Question 14

Use synthetic division to decide whether the given number k is a zero of the given polynomial function.
-$k = 2 - 3 i ; f ( x ) = x ^ { 2 } + 4 x + 13$

Accepted Answer

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

Question 15

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

Accepted Answer

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

Question 16

Find the equation that the given graph represents.
-$$f ( x ) = - ( x + 4 ) ^ { 2 }$$

Accepted Answer

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

Question 17

Graph the function.
-$$f ( x ) = 2 - \frac { 2 } { x }$$

Accepted Answer

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

Question 18

Solve the problem
-A rock is propelled upward from the top of a building 160 feet tall at an initial velocity of 200 feet per second. Give the function that describes the height of the rocket in terms of time $t$.

Accepted Answer

A)  $f ( t ) = - 200 t ^ { 2 } + 16 t + 160$ 
B)  $f ( t ) = - 16 t ^ { 2 } + 200 t + 160$ 
C)  $f ( t ) = 16 t ^ { 2 } + 200 t + 160$ 
D)  $f ( t ) = - 16 t ^ { 2 } + 160 t + 200$ 
A)  $f ( t ) = - 200 t ^ { 2 } + 16 t + 160$ 
B)  $f ( t ) = - 16 t ^ { 2 } + 200 t + 160$ 
C)  $f ( t ) = 16 t ^ { 2 } + 200 t + 160$ 
D)  $f ( t ) = - 16 t ^ { 2 } + 160 t + 200$

Question 19

Provide an appropriate response.
-How many real zeros does this graph have?

Accepted Answer

A)  1 
B)  2 
C)  3 
D)  4 
A)  1 
B)  2 
C)  3 
D)  4

Question 20

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary.
-$$f ( x ) = x ^ { 4 } - 10 x ^ { 3 } + 23 x ^ { 2 } - 10 x + 22$$

Accepted Answer

A)  $i , - i , 1 + \sqrt { 3 } , 1 - \sqrt { 3 }$ 
B)  i, $- \mathrm { i } , 5 + 2 \sqrt { 3 } , 5 - 2 \sqrt { 3 }$ 
C)  $\mathrm { i } , - \mathrm { i } , 5 + \sqrt { 3 } , 5 - \sqrt { 3 }$ 
D)  $\mathrm { i } , - \mathrm { i } , - 5 + \sqrt { 3 } , - 5 - \sqrt { 3 }$ 
A)  $i , - i , 1 + \sqrt { 3 } , 1 - \sqrt { 3 }$ 
B)  i, $- \mathrm { i } , 5 + 2 \sqrt { 3 } , 5 - 2 \sqrt { 3 }$ 
C)  $\mathrm { i } , - \mathrm { i } , 5 + \sqrt { 3 } , 5 - \sqrt { 3 }$ 
D)  $\mathrm { i } , - \mathrm { i } , - 5 + \sqrt { 3 } , - 5 - \sqrt { 3 }$

Find the equation that the given graph represents. - $f ( x ) = x ^ { 3 } + 2$ $Find the equation that the given graph represents. - f ( x ) = x ^ { 3 } + 2$

Give all possible rational zeros for the following polynomial. - $P ( x ) = 22 x ^ { 3 } + 88 x ^ { 2 } + 2 x - 11$

Use the intermediate value theorem for polynomials to show that the polynomial function has a real zero between the numbers given. - $f ( x ) = 6 x ^ { 3 } - 10 x + 7 ; - 2 \text { and } - 1$

Use the graph to answer the question. -Find the domain of the rational function graphed below. An

Match the equation to the correct graph. - $y = 2 ( x - 1 ) ^ { 2 } - 2$

Provide an appropriate response. -For what values of a does the quadratic function $f ( x ) = a x ^ { 2 } + 4 x + 5$ have two $x$ -intercepts?

Identify the vertex of the parabola. - $f ( x ) = ( x - 4 ) ^ { 2 }$

Use the factor theorem to decide whether or not the second polynomial is a factor of the first. - $x ^ { 3 } - 3 x ^ { 2 } + 7 x - 5 ; x - 1$

Use the boundedness theorem to determine whether the polynomial function satisfies the given condition. -The polynomial $f ( x ) = x ^ { 4 } - x ^ { 3 } + 2 x ^ { 2 } - 4 x - 10$ has no real zero greater than 3 .

Find an equation for the rational function graph. -

Find an equation for the rational function graph. -

Use synthetic division to decide whether the given number k is a zero of the given polynomial function. - $k = 2 - 3 i ; f ( x ) = x ^ { 2 } + 4 x + 13$

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

Find the equation that the given graph represents. - $f ( x ) = - ( x + 4 ) ^ { 2 }$ $Find the equation that the given graph represents. - f ( x ) = - ( x + 4 ) ^ { 2 }$

Graph the function. - $f ( x ) = 2 - \frac { 2 } { x }$ $Graph the function. - f ( x ) = 2 - \frac { 2 } { x }$

Solve the problem -A rock is propelled upward from the top of a building 160 feet tall at an initial velocity of 200 feet per second. Give the function that describes the height of the rocket in terms of time $t$ .

Provide an appropriate response. -How many real zeros does this graph have?

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary. - $f ( x ) = x ^ { 4 } - 10 x ^ { 3 } + 23 x ^ { 2 } - 10 x + 22$

Review of Basic Concepts

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

Filters

Exam 4: Polynomial and Rational Functions

Find the equation that the given graph represents. - f(x)=x3+2f ( x ) = x ^ { 3 } + 2f(x)=x3+2

Give all possible rational zeros for the following polynomial. - P(x)=22x3+88x2+2x−11P ( x ) = 22 x ^ { 3 } + 88 x ^ { 2 } + 2 x - 11P(x)=22x3+88x2+2x−11

Use the intermediate value theorem for polynomials to show that the polynomial function has a real zero between the numbers given. - f(x)=6x3−10x+7;−2 and −1f ( x ) = 6 x ^ { 3 } - 10 x + 7 ; - 2 \text { and } - 1f(x)=6x3−10x+7;−2 and −1

Use the graph to answer the question. -Find the domain of the rational function graphed below. An

Match the equation to the correct graph. - y=2(x−1)2−2y = 2 ( x - 1 ) ^ { 2 } - 2y=2(x−1)2−2

Provide an appropriate response. -For what values of a does the quadratic function f(x)=ax2+4x+5f ( x ) = a x ^ { 2 } + 4 x + 5f(x)=ax2+4x+5 have two xxx -intercepts?

Identify the vertex of the parabola. - f(x)=(x−4)2f ( x ) = ( x - 4 ) ^ { 2 }f(x)=(x−4)2

Use the factor theorem to decide whether or not the second polynomial is a factor of the first. - x3−3x2+7x−5;x−1x ^ { 3 } - 3 x ^ { 2 } + 7 x - 5 ; x - 1x3−3x2+7x−5;x−1

Use the boundedness theorem to determine whether the polynomial function satisfies the given condition. -The polynomial f(x)=x4−x3+2x2−4x−10f ( x ) = x ^ { 4 } - x ^ { 3 } + 2 x ^ { 2 } - 4 x - 10f(x)=x4−x3+2x2−4x−10 has no real zero greater than 3 .

Find an equation for the rational function graph. -

Use the equation and the corresponding graph for the quadratic function to find what is requested. - f(x)=(x−3)2−2f ( x ) = ( x - 3 ) ^ { 2 } - 2f(x)=(x−3)2−2 Find the coordinates of the vertex.

Find an equation for the rational function graph. -

Use the equation and the corresponding graph for the quadratic function to find what is requested. - f(x)=(x−5)2−2f(x)=(x-5)^{2}-2f(x)=(x−5)2−2 Find the equation of the axis.

Use synthetic division to decide whether the given number k is a zero of the given polynomial function. - k=2−3i;f(x)=x2+4x+13k = 2 - 3 i ; f ( x ) = x ^ { 2 } + 4 x + 13k=2−3i;f(x)=x2+4x+13

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

Find the equation that the given graph represents. - f(x)=−(x+4)2f ( x ) = - ( x + 4 ) ^ { 2 }f(x)=−(x+4)2

Graph the function. - f(x)=2−2xf ( x ) = 2 - \frac { 2 } { x }f(x)=2−x2​

Solve the problem -A rock is propelled upward from the top of a building 160 feet tall at an initial velocity of 200 feet per second. Give the function that describes the height of the rocket in terms of time ttt .

Provide an appropriate response. -How many real zeros does this graph have?

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary. - f(x)=x4−10x3+23x2−10x+22f ( x ) = x ^ { 4 } - 10 x ^ { 3 } + 23 x ^ { 2 } - 10 x + 22f(x)=x4−10x3+23x2−10x+22

Review of Basic Concepts

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

Filters

Find the equation that the given graph represents. - $f ( x ) = x ^ { 3 } + 2$ $Find the equation that the given graph represents. - f ( x ) = x ^ { 3 } + 2$

Give all possible rational zeros for the following polynomial. - $P ( x ) = 22 x ^ { 3 } + 88 x ^ { 2 } + 2 x - 11$

Use the intermediate value theorem for polynomials to show that the polynomial function has a real zero between the numbers given. - $f ( x ) = 6 x ^ { 3 } - 10 x + 7 ; - 2 \text { and } - 1$

Match the equation to the correct graph. - $y = 2 ( x - 1 ) ^ { 2 } - 2$

Provide an appropriate response. -For what values of a does the quadratic function $f ( x ) = a x ^ { 2 } + 4 x + 5$ have two $x$ -intercepts?

Identify the vertex of the parabola. - $f ( x ) = ( x - 4 ) ^ { 2 }$

Use the factor theorem to decide whether or not the second polynomial is a factor of the first. - $x ^ { 3 } - 3 x ^ { 2 } + 7 x - 5 ; x - 1$

Use the boundedness theorem to determine whether the polynomial function satisfies the given condition. -The polynomial $f ( x ) = x ^ { 4 } - x ^ { 3 } + 2 x ^ { 2 } - 4 x - 10$ has no real zero greater than 3 .

Use synthetic division to decide whether the given number k is a zero of the given polynomial function. - $k = 2 - 3 i ; f ( x ) = x ^ { 2 } + 4 x + 13$

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

Find the equation that the given graph represents. - $f ( x ) = - ( x + 4 ) ^ { 2 }$ $Find the equation that the given graph represents. - f ( x ) = - ( x + 4 ) ^ { 2 }$

Graph the function. - $f ( x ) = 2 - \frac { 2 } { x }$ $Graph the function. - f ( x ) = 2 - \frac { 2 } { x }$

Solve the problem -A rock is propelled upward from the top of a building 160 feet tall at an initial velocity of 200 feet per second. Give the function that describes the height of the rocket in terms of time $t$ .

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary. - $f ( x ) = x ^ { 4 } - 10 x ^ { 3 } + 23 x ^ { 2 } - 10 x + 22$