Question 1

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

Accepted Answer

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

Question 2

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

Accepted Answer

A) True 
 B)False

Question 3

Round your answer to two decimal places.
-The amount of tread left on a tire varies inversely as the number of miles the tire has traveled. A tire that has traveled $66,000 \mathrm { mi }$ has $\frac { 1 } { 32 } \mathrm { in }$. of tread left. How much tread will be left on a tire that has traveled 21,000 mi?

Accepted Answer

A)  2,112,000 in. 
B)  $\frac { 1 } { 2112000 }$ in. 
C)  $\frac { 112 } { 11 } \mathrm { in }$. 
D)  $\frac { 11 } { 112 }$ in. 
A)  2,112,000 in. 
B)  $\frac { 1 } { 2112000 }$ in. 
C)  $\frac { 112 } { 11 } \mathrm { in }$. 
D)  $\frac { 11 } { 112 }$ in.

Question 4

Find the equation of the axis of symmetry of the parabola.
-$$f ( x ) = ( x + 5 ) ^ { 2 } + 7$$

Accepted Answer

A)  $y = - 5$ 
B)  $y = 0$ 
C)  $x = - 5$ 
D)  $x = 5$ 
A)  $y = - 5$ 
B)  $y = 0$ 
C)  $x = - 5$ 
D)  $x = 5$

Question 5

Determine which of the rational functions given below has the following feature(s).
-The x-axis is its horizontal asymptote

Accepted Answer

A)  $f ( x ) = \frac { 5 x - 1 } { x + 9 }$ 
B)  $f ( x ) = \frac { 9 } { x - 5 }$ 
C)  $f ( x ) = \frac { x - 5 } { x }$ 
D)  $f ( x ) = \frac { x + 5 } { x + 9 }$ 
A)  $f ( x ) = \frac { 5 x - 1 } { x + 9 }$ 
B)  $f ( x ) = \frac { 9 } { x - 5 }$ 
C)  $f ( x ) = \frac { x - 5 } { x }$ 
D)  $f ( x ) = \frac { x + 5 } { x + 9 }$

Question 6

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary.
-$$f ( x ) = x ^ { 4 } - 36$$

Accepted Answer

A)  $\sqrt { 6 } , - \sqrt { 6 }$ 
B)  $\sqrt { 6 } , - \sqrt { 6 } i , \sqrt { 6 } i , - \sqrt { 6 }$ 
C)  $\sqrt { 6 } , \sqrt { 6 } i$ 
D)  $\sqrt { 6 } , - 6 i , 6 i , - \sqrt { 6 }$ 
A)  $\sqrt { 6 } , - \sqrt { 6 }$ 
B)  $\sqrt { 6 } , - \sqrt { 6 } i , \sqrt { 6 } i , - \sqrt { 6 }$ 
C)  $\sqrt { 6 } , \sqrt { 6 } i$ 
D)  $\sqrt { 6 } , - 6 i , 6 i , - \sqrt { 6 }$

Question 7

Give the equation of any oblique asymptotes.
-$$f ( x ) = \frac { x ^ { 2 } + 7 x + 4 } { x + 6 }$$

Accepted Answer

A)  $y = x + 1$ 
B)  $x = y + 1$ 
C)  $y = x - 13$ 
D)  none 
A)  $y = x + 1$ 
B)  $x = y + 1$ 
C)  $y = x - 13$ 
D)  none

Question 8

Determine whether the statement is true or false.
-If f(x) is a polynomial and f(-5) = 0, then x + 5 is a factor of f(x).

Accepted Answer

A) True 
 B)False

Question 9

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

Accepted Answer

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

Question 10

Graph the polynomial function. Factor first if the expression is not in factored form.
-$$\begin{aligned}
\mathrm { f } ( \mathrm { x } ) = \mathrm { x } ^ { 3 } + 4 \mathrm { x } ^ { 2 } - \mathrm { x } - 4 \

\end{aligned}$$

Accepted Answer

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

Question 11

Translate the given formula to an English phrase using the word "varies".
-$$r = \frac { d } { t } \text {, where } r \text { is the rate by which distance } d \text { is covered in time } t$$

Accepted Answer

Rate varies directly

Question 12

Find a polynomial function f(x) of least possible degree having the graph shown.
-

Accepted Answer

A)  $f ( x ) = ( x + 3 ) ( x - 1 )$ 
B)  $f ( x ) = ( x + 3 ) ( x - 1 ) ( x - 4 )$ 
C)  $f ( x ) = \frac { 1 } { 3 } ( x - 3 ) ( x + 1 ) ( x + 4 )$ 
D)  $f ( x ) = \frac { 1 } { 3 } ( x + 3 ) ( x - 1 ) ( x - 4 )$ 
A)  $f ( x ) = ( x + 3 ) ( x - 1 )$ 
B)  $f ( x ) = ( x + 3 ) ( x - 1 ) ( x - 4 )$ 
C)  $f ( x ) = \frac { 1 } { 3 } ( x - 3 ) ( x + 1 ) ( x + 4 )$ 
D)  $f ( x ) = \frac { 1 } { 3 } ( x + 3 ) ( x - 1 ) ( x - 4 )$

Question 13

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

Accepted Answer

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

Question 14

Use a graphing calculator to find the coordinates of the turning points of the graph of the polynomial function in the
indicated domain interval. Give answers to the nearest hundredth.
-$$f ( x ) = x ^ { 3 } + 8 x ^ { 2 } - 21 x - 108 ; [ 1,2 ]$$

Accepted Answer

A)  $( 0,12 )$ 
B)  $( 3.50 , - 40.62 )$ 
C)  $( - 6.42,91.94 )$ 
D)  $( 1.09 , - 120.09 )$ 
A)  $( 0,12 )$ 
B)  $( 3.50 , - 40.62 )$ 
C)  $( - 6.42,91.94 )$ 
D)  $( 1.09 , - 120.09 )$

Question 15

Sketch the graph of the parabola.
-$$y = \frac { 2 } { 5 } x ^ { 2 } - 1$$

Accepted Answer

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

Question 16

Translate the given formula to an English phrase using the word "varies".
-$$C = 2 \pi r \text {, where } C \text { is the circumference of a circle of radius } r$$

Accepted Answer

The circumference of

Question 17

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

Accepted Answer

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

Question 18

Solve the problem
-The population of a city has varied considerably in recent years. The data in the table relates the population P to time t, in years. Use a quadratic function fitted to the data to predict the population in year 10. $$\begin{array} { c | c } 
\text { Year, t } & \text { Population, P } \
\hline 0 & 59,000 \
\hline 1 & 48,000 \
\hline 2 & 43,500 \
\hline 3 & 49,000 \
\hline 4 & 41,500 \
\hline 5 & 39,000 \
\hline 6 & 42,500
\end{array}$$

Accepted Answer

A)  48,431 
B)  58,964 
C)  119,000 
D)  81,202 
A)  48,431 
B)  58,964 
C)  119,000 
D)  81,202

Question 19

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

Accepted Answer

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

Question 20

Provide an appropriate response.
-For what value of $c$ does the quadratic function $f ( x ) = 3 x ^ { 2 } + 8 x + c$ have exactly one $x$-intercept?

Accepted Answer

A)  $\frac { 2 } { 3 }$ 
B)  $- \frac { 2 } { 3 }$ 
C)  16 
D)  $\frac { 16 } { 3 }$ 
A)  $\frac { 2 } { 3 }$ 
B)  $- \frac { 2 } { 3 }$ 
C)  16 
D)  $\frac { 16 } { 3 }$

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

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

Find the equation of the axis of symmetry of the parabola. - $f ( x ) = ( x + 5 ) ^ { 2 } + 7$

Determine which of the rational functions given below has the following feature(s). -The x-axis is its horizontal asymptote

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary. - $f ( x ) = x ^ { 4 } - 36$

Give the equation of any oblique asymptotes. - $f ( x ) = \frac { x ^ { 2 } + 7 x + 4 } { x + 6 }$

Determine whether the statement is true or false. -If f(x) is a polynomial and f(-5) = 0, then x + 5 is a factor of f(x).

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

Translate the given formula to an English phrase using the word "varies". - $r = \frac { d } { t } \text {, where } r \text { is the rate by which distance } d \text { is covered in time } t$

Find a polynomial function f(x) of least possible degree having the graph shown. -

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

Use a graphing calculator to find the coordinates of the turning points of the graph of the polynomial function in the indicated domain interval. Give answers to the nearest hundredth. - $f ( x ) = x ^ { 3 } + 8 x ^ { 2 } - 21 x - 108 ; [ 1,2 ]$

Sketch the graph of the parabola. - $y = \frac { 2 } { 5 } x ^ { 2 } - 1$ $Sketch the graph of the parabola. - y = \frac { 2 } { 5 } x ^ { 2 } - 1$

Translate the given formula to an English phrase using the word "varies". - $C = 2 \pi r \text {, where } C \text { is the circumference of a circle of radius } r$

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

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

Provide an appropriate response. -For what value of $c$ does the quadratic function $f ( x ) = 3 x ^ { 2 } + 8 x + c$ have exactly one $x$ -intercept?

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

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

Determine whether the statement is true or false. - The function f(x)=1x is decreasing on the interval (−∞,∞)\text { The function } f ( x ) = \frac { 1 } { x } \text { is decreasing on the interval } ( - \infty , \infty ) The function f(x)=x1​ is decreasing on the interval (−∞,∞)

Find the equation of the axis of symmetry of the parabola. - f(x)=(x+5)2+7f ( x ) = ( x + 5 ) ^ { 2 } + 7f(x)=(x+5)2+7

Determine which of the rational functions given below has the following feature(s). -The x-axis is its horizontal asymptote

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary. - f(x)=x4−36f ( x ) = x ^ { 4 } - 36f(x)=x4−36

Give the equation of any oblique asymptotes. - f(x)=x2+7x+4x+6f ( x ) = \frac { x ^ { 2 } + 7 x + 4 } { x + 6 }f(x)=x+6x2+7x+4​

Determine whether the statement is true or false. -If f(x) is a polynomial and f(-5) = 0, then x + 5 is a factor of f(x).

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

Graph the polynomial function. Factor first if the expression is not in factored form. - ()=+4--4

Find a polynomial function f(x) of least possible degree having the graph shown. -

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

Sketch the graph of the parabola. - y=25x2−1y = \frac { 2 } { 5 } x ^ { 2 } - 1y=52​x2−1

Translate the given formula to an English phrase using the word "varies". - C=2πr, where C is the circumference of a circle of radius rC = 2 \pi r \text {, where } C \text { is the circumference of a circle of radius } rC=2πr, where C is the circumference of a circle of radius r

Sketch the graph of the parabola. - y=x2−2x+1y = x ^ { 2 } - 2 x + 1y=x2−2x+1

Graph the function. - f(x)=2x+2f ( x ) = \frac { 2 } { x + 2 }f(x)=x+22​

Provide an appropriate response. -For what value of ccc does the quadratic function f(x)=3x2+8x+cf ( x ) = 3 x ^ { 2 } + 8 x + cf(x)=3x2+8x+c have exactly one xxx -intercept?

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

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

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

Find the equation of the axis of symmetry of the parabola. - $f ( x ) = ( x + 5 ) ^ { 2 } + 7$

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary. - $f ( x ) = x ^ { 4 } - 36$

Give the equation of any oblique asymptotes. - $f ( x ) = \frac { x ^ { 2 } + 7 x + 4 } { x + 6 }$

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

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

Sketch the graph of the parabola. - $y = \frac { 2 } { 5 } x ^ { 2 } - 1$ $Sketch the graph of the parabola. - y = \frac { 2 } { 5 } x ^ { 2 } - 1$

Translate the given formula to an English phrase using the word "varies". - $C = 2 \pi r \text {, where } C \text { is the circumference of a circle of radius } r$

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

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

Provide an appropriate response. -For what value of $c$ does the quadratic function $f ( x ) = 3 x ^ { 2 } + 8 x + c$ have exactly one $x$ -intercept?