Question 1

Solve the problem.
-y varies directly as z and y = 120 when z = 10. Find y when z is 18.

Accepted Answer

A)  144 
B)  100 
C)  216 
D)  324 
A)  144 
B)  100 
C)  216 
D)  324

Question 2

Solve the problem.
-The population of a small town is given by the table.

If the population is modeled by $\mathrm { p } ( \mathrm { t } ) = \mathrm { at } ^ { 2 } + \mathrm { b }$ where $\mathrm { t }$ is in years and $\mathrm { t } = 0$ corresponds to the year 1980 and $t = 1$ corresponds the year 1990 , find $a$.

Accepted Answer

A)  11 
B)  18 
C)  9 
D)  22 
A)  11 
B)  18 
C)  9 
D)  22

Question 3

Find the domain and range of the function.
-$$y = ( x + 8 ) ^ { 2 } + 3$$

Accepted Answer

A)  Domain: $[ 3 , \infty )$; Range: $[ - \infty , 3 )$ 
B)  Domain: $( - \infty , \infty )$; Range: $[ - 8 , \infty )$ 
C)  Domain: $[ - 8 , \infty )$; Range: $[ - \infty , 8 )$ 
D)  Domain: $( - \infty , \infty )$; Range: $[ 3 , \infty )$ 
A)  Domain: $[ 3 , \infty )$; Range: $[ - \infty , 3 )$ 
B)  Domain: $( - \infty , \infty )$; Range: $[ - 8 , \infty )$ 
C)  Domain: $[ - 8 , \infty )$; Range: $[ - \infty , 8 )$ 
D)  Domain: $( - \infty , \infty )$; Range: $[ 3 , \infty )$

Question 4

Solve the problem.
-The graph of $f ( x ) = - x ^ { 4 } + x ^ { 3 } + 8 x ^ { 2 } - 12 x$ is shown below. Use the graph to factor $f ( x )$.

Accepted Answer

A)  $f ( x ) = - x ( x - 2 ) ( x + 3 ) ^ { 2 }$ 
B)  $f ( x ) = - x ( x + 3 ) ( x - 2 ) ^ { 2 }$ 
C)  $f ( x ) = - x ( x - 3 ) ( x + 2 ) ^ { 2 }$ 
D)  $f ( x ) = x ( x + 3 ) ( x - 2 ) ^ { 2 }$ 
A)  $f ( x ) = - x ( x - 2 ) ( x + 3 ) ^ { 2 }$ 
B)  $f ( x ) = - x ( x + 3 ) ( x - 2 ) ^ { 2 }$ 
C)  $f ( x ) = - x ( x - 3 ) ( x + 2 ) ^ { 2 }$ 
D)  $f ( x ) = x ( x + 3 ) ( x - 2 ) ^ { 2 }$

Question 5

Given the equation or other information for a parabola, find the matching description or graph.
-$\begin{array}{l}
f(x)=a x^{2}+b x+c \
a>0 ; b^{2}-4 a c>0
\end{array}$

Accepted Answer

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

Question 6

Use synthetic division to perform the division.
-$$\frac { x ^ { 4 } + 8 x ^ { 3 } + 12 x ^ { 2 } - 13 x + 10 } { x + 5 }$$

Accepted Answer

A)  $x ^ { 3 } + 3 x ^ { 2 } - 6 x + 4$ 
B)  $x ^ { 3 } + 3 x ^ { 2 } - 6 x$ 
C)  $x ^ { 3 } + 3 x ^ { 2 } - 3 x + 2$ 
D)  $x ^ { 3 } + 4 x ^ { 2 } - 3 x - 2$ 
A)  $x ^ { 3 } + 3 x ^ { 2 } - 6 x + 4$ 
B)  $x ^ { 3 } + 3 x ^ { 2 } - 6 x$ 
C)  $x ^ { 3 } + 3 x ^ { 2 } - 3 x + 2$ 
D)  $x ^ { 3 } + 4 x ^ { 2 } - 3 x - 2$

Question 7

Find the equation of the axis of symmetry of the parabola.
-$$f ( x ) = x ^ { 2 } + 8$$

Accepted Answer

A)  $y = 8$ 
B)  $x = 8$ 
C)  $x = - 8$ 
D)  $x = 0$ 
A)  $y = 8$ 
B)  $x = 8$ 
C)  $x = - 8$ 
D)  $x = 0$

Question 8

Sketch the graph of the parabola.
-$y=-\frac{1}{2} x^{2}-7$

Accepted Answer

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

Question 9

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

Accepted Answer

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

Question 10

Sketch the graph of the rational function.
-$f(x)=\frac{5 x}{(x-3)(x-4)}$

Accepted Answer

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

Question 11

Use synthetic division to decide whether the given number k is a zero of the given polynomial function.
-$5 i ; f ( x ) = x ^ { 3 } + 2 x ^ { 2 } + 25 x + 50$

Accepted Answer

A)  Yes 
B)  $\mathrm { No }$ 
A)  Yes 
B)  $\mathrm { No }$

Question 12

Solve the inequality. Write the solution set in interval notation.
-$$\mathrm { x } ^ { 2 } + 3 \mathrm { x } - 18 < 0$$

Accepted Answer

A)  $( - 3,6 )$ 
B)  $( - \infty , - 6 ) \cup ( 3 , \infty )$ 
C)  $( - 6,3 )$ 
D)  $( - \infty , - 3 ) \cup ( 6 , \infty )$ 
A)  $( - 3,6 )$ 
B)  $( - \infty , - 6 ) \cup ( 3 , \infty )$ 
C)  $( - 6,3 )$ 
D)  $( - \infty , - 3 ) \cup ( 6 , \infty )$

Question 13

Give the equatiosn of any horizontal asymptotes.
-$$h ( x ) = \frac { 4 x ^ { 2 } - 5 x - 9 } { 5 x ^ { 2 } - 6 x + 8 }$$

Accepted Answer

A)  $y = \frac { 5 } { 6 }$ 
B)  $\mathrm { y } = 0$ 
C)  none 
D)  $\mathrm { y } = \frac { 4 } { 5 }$ 
A)  $y = \frac { 5 } { 6 }$ 
B)  $\mathrm { y } = 0$ 
C)  none 
D)  $\mathrm { y } = \frac { 4 } { 5 }$

Question 14

Solve.
-The data in the table show the number of burglaries reported in a small town for several years on record.

Determine the linear, quadratic, cubic, or quartic function that best fits the data.

Accepted Answer

A)  $f ( x ) = 0.28 x + 1.7$ 
B)  $f ( x ) = - 0.0007 x ^ { 3 } + 0.086 x ^ { 2 } - 0.79 x + 4.07$ 
C)  $f ( x ) = 0.07 x ^ { 2 } - 0.71 x + 3.99$ 
D)  $f ( x ) = - 0.00004 x ^ { 4 } + 0.0006 x ^ { 3 } + 0.07 x ^ { 2 } - 0.76 x + 4.05$ 
A)  $f ( x ) = 0.28 x + 1.7$ 
B)  $f ( x ) = - 0.0007 x ^ { 3 } + 0.086 x ^ { 2 } - 0.79 x + 4.07$ 
C)  $f ( x ) = 0.07 x ^ { 2 } - 0.71 x + 3.99$ 
D)  $f ( x ) = - 0.00004 x ^ { 4 } + 0.0006 x ^ { 3 } + 0.07 x ^ { 2 } - 0.76 x + 4.05$

Question 15

Translate the given formula to an English phrase using the word ʺvariesʺ.
-$$V = \pi r ^ { 2 } h \text {, where } V \text { is the volume of a cylinder of radius } r \text { and height }$$

Accepted Answer

The volume of a cyli

Question 16

Determine whether the statement is true or false.
-If f(x) is a polynomial having only real coefficients and 1 - 4i is a zero of f(x), then -1 + 4i is also
zero.

Accepted Answer

A) True 
 B)False

Question 17

Write the word or phrase that best completes each statement or answers the question.
-The domain of a polynomial function is the set of all real numbers. What is the range of a polynomial function of odd degree? One of even degree?

Accepted Answer

The answer of Write the word or phrase that best...

Question 18

Sketch the graph of the parabola.
-$f(x)=(x+5)^{2}$

Accepted Answer

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

Question 19

Use synthetic division to decide whether the given number k is a zero of the given polynomial function.
-$$- 2 ; f ( x ) = x ^ { 4 } - 6 x ^ { 2 } + 8$$

Accepted Answer

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

Question 20

Graph the polynomial function. Factor first if the expression is not in factored form.
-$$f ( x ) = x \left( x ^ { 2 } - 9 \right) ( x + 1 ) ^ { 3 }$$

Accepted Answer

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

Solve the problem. -y varies directly as z and y = 120 when z = 10. Find y when z is 18.

Find the domain and range of the function. - $y = ( x + 8 ) ^ { 2 } + 3$

Solve the problem. -The graph of $f ( x ) = - x ^ { 4 } + x ^ { 3 } + 8 x ^ { 2 } - 12 x$ is shown below. Use the graph to factor $f ( x )$ . $Solve the problem. -The graph of f ( x ) = - x ^ { 4 } + x ^ { 3 } + 8 x ^ { 2 } - 12 x is shown below. Use the graph to factor f ( x ) .$

Given the equation or other information for a parabola, find the matching description or graph. - f(x)=a+bx+c a>0;-4ac>0

Use synthetic division to perform the division. - $\frac { x ^ { 4 } + 8 x ^ { 3 } + 12 x ^ { 2 } - 13 x + 10 } { x + 5 }$

Find the equation of the axis of symmetry of the parabola. - $f ( x ) = x ^ { 2 } + 8$

Sketch the graph of the parabola. - $y=-\frac{1}{2} x^{2}-7$ $Sketch the graph of the parabola. - y=-\frac{1}{2} x^{2}-7$

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

Sketch the graph of the rational function. - $f(x)=\frac{5 x}{(x-3)(x-4)}$ $Sketch the graph of the rational function. - f(x)=\frac{5 x}{(x-3)(x-4)}$

Use synthetic division to decide whether the given number k is a zero of the given polynomial function. - $5 i ; f ( x ) = x ^ { 3 } + 2 x ^ { 2 } + 25 x + 50$

Solve the inequality. Write the solution set in interval notation. - $\mathrm { x } ^ { 2 } + 3 \mathrm { x } - 18 < 0$

Give the equatiosn of any horizontal asymptotes. - $h ( x ) = \frac { 4 x ^ { 2 } - 5 x - 9 } { 5 x ^ { 2 } - 6 x + 8 }$

Solve. -The data in the table show the number of burglaries reported in a small town for several years on record. Determine the linear, quadratic, cubic, or quartic function that best fits the data.

Translate the given formula to an English phrase using the word ʺvariesʺ. - $V = \pi r ^ { 2 } h \text {, where } V \text { is the volume of a cylinder of radius } r \text { and height }$

Determine whether the statement is true or false. -If f(x) is a polynomial having only real coefficients and 1 - 4i is a zero of f(x), then -1 + 4i is also zero.

Write the word or phrase that best completes each statement or answers the question. -The domain of a polynomial function is the set of all real numbers. What is the range of a polynomial function of odd degree? One of even degree?

Sketch the graph of the parabola. - $f(x)=(x+5)^{2}$ $Sketch the graph of the parabola. - f(x)=(x+5)^{2}$

Use synthetic division to decide whether the given number k is a zero of the given polynomial function. - $- 2 ; f ( x ) = x ^ { 4 } - 6 x ^ { 2 } + 8$

Graph the polynomial function. Factor first if the expression is not in factored form. - $f ( x ) = x \left( x ^ { 2 } - 9 \right) ( x + 1 ) ^ { 3 }$ $Graph the polynomial function. Factor first if the expression is not in factored form. - f ( x ) = x \left( x ^ { 2 } - 9 \right) ( x + 1 ) ^ { 3 }$

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

Solve the problem. -y varies directly as z and y = 120 when z = 10. Find y when z is 18.

Find the domain and range of the function. - y=(x+8)2+3y = ( x + 8 ) ^ { 2 } + 3y=(x+8)2+3

Solve the problem. -The graph of f(x)=−x4+x3+8x2−12xf ( x ) = - x ^ { 4 } + x ^ { 3 } + 8 x ^ { 2 } - 12 xf(x)=−x4+x3+8x2−12x is shown below. Use the graph to factor f(x)f ( x )f(x) .

Given the equation or other information for a parabola, find the matching description or graph. - f(x)=a+bx+c a>0;-4ac>0

Use synthetic division to perform the division. - x4+8x3+12x2−13x+10x+5\frac { x ^ { 4 } + 8 x ^ { 3 } + 12 x ^ { 2 } - 13 x + 10 } { x + 5 }x+5x4+8x3+12x2−13x+10​

Find the equation of the axis of symmetry of the parabola. - f(x)=x2+8f ( x ) = x ^ { 2 } + 8f(x)=x2+8

Sketch the graph of the parabola. - y=−12x2−7y=-\frac{1}{2} x^{2}-7y=−21​x2−7

Solve the problem. - f(x)=3x3f(x)=3 x^{3}f(x)=3x3

Sketch the graph of the rational function. - f(x)=5x(x−3)(x−4)f(x)=\frac{5 x}{(x-3)(x-4)}f(x)=(x−3)(x−4)5x​

Use synthetic division to decide whether the given number k is a zero of the given polynomial function. - 5i;f(x)=x3+2x2+25x+505 i ; f ( x ) = x ^ { 3 } + 2 x ^ { 2 } + 25 x + 505i;f(x)=x3+2x2+25x+50

Solve the inequality. Write the solution set in interval notation. - x2+3x−18<0\mathrm { x } ^ { 2 } + 3 \mathrm { x } - 18 < 0x2+3x−18<0

Give the equatiosn of any horizontal asymptotes. - h(x)=4x2−5x−95x2−6x+8h ( x ) = \frac { 4 x ^ { 2 } - 5 x - 9 } { 5 x ^ { 2 } - 6 x + 8 }h(x)=5x2−6x+84x2−5x−9​

Solve. -The data in the table show the number of burglaries reported in a small town for several years on record. Determine the linear, quadratic, cubic, or quartic function that best fits the data.

Determine whether the statement is true or false. -If f(x) is a polynomial having only real coefficients and 1 - 4i is a zero of f(x), then -1 + 4i is also zero.

Write the word or phrase that best completes each statement or answers the question. -The domain of a polynomial function is the set of all real numbers. What is the range of a polynomial function of odd degree? One of even degree?

Sketch the graph of the parabola. - f(x)=(x+5)2f(x)=(x+5)^{2}f(x)=(x+5)2

Use synthetic division to decide whether the given number k is a zero of the given polynomial function. - −2;f(x)=x4−6x2+8- 2 ; f ( x ) = x ^ { 4 } - 6 x ^ { 2 } + 8−2;f(x)=x4−6x2+8

Graph the polynomial function. Factor first if the expression is not in factored form. - f(x)=x(x2−9)(x+1)3f ( x ) = x \left( x ^ { 2 } - 9 \right) ( x + 1 ) ^ { 3 }f(x)=x(x2−9)(x+1)3

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

Find the domain and range of the function. - $y = ( x + 8 ) ^ { 2 } + 3$

Solve the problem. -The graph of $f ( x ) = - x ^ { 4 } + x ^ { 3 } + 8 x ^ { 2 } - 12 x$ is shown below. Use the graph to factor $f ( x )$ . $Solve the problem. -The graph of f ( x ) = - x ^ { 4 } + x ^ { 3 } + 8 x ^ { 2 } - 12 x is shown below. Use the graph to factor f ( x ) .$

Use synthetic division to perform the division. - $\frac { x ^ { 4 } + 8 x ^ { 3 } + 12 x ^ { 2 } - 13 x + 10 } { x + 5 }$

Find the equation of the axis of symmetry of the parabola. - $f ( x ) = x ^ { 2 } + 8$

Sketch the graph of the parabola. - $y=-\frac{1}{2} x^{2}-7$ $Sketch the graph of the parabola. - y=-\frac{1}{2} x^{2}-7$

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

Sketch the graph of the rational function. - $f(x)=\frac{5 x}{(x-3)(x-4)}$ $Sketch the graph of the rational function. - f(x)=\frac{5 x}{(x-3)(x-4)}$

Use synthetic division to decide whether the given number k is a zero of the given polynomial function. - $5 i ; f ( x ) = x ^ { 3 } + 2 x ^ { 2 } + 25 x + 50$

Solve the inequality. Write the solution set in interval notation. - $\mathrm { x } ^ { 2 } + 3 \mathrm { x } - 18 < 0$

Give the equatiosn of any horizontal asymptotes. - $h ( x ) = \frac { 4 x ^ { 2 } - 5 x - 9 } { 5 x ^ { 2 } - 6 x + 8 }$

Sketch the graph of the parabola. - $f(x)=(x+5)^{2}$ $Sketch the graph of the parabola. - f(x)=(x+5)^{2}$

Use synthetic division to decide whether the given number k is a zero of the given polynomial function. - $- 2 ; f ( x ) = x ^ { 4 } - 6 x ^ { 2 } + 8$

Graph the polynomial function. Factor first if the expression is not in factored form. - $f ( x ) = x \left( x ^ { 2 } - 9 \right) ( x + 1 ) ^ { 3 }$ $Graph the polynomial function. Factor first if the expression is not in factored form. - f ( x ) = x \left( x ^ { 2 } - 9 \right) ( x + 1 ) ^ { 3 }$