Question 1

Use synthetic division to decide whether the given number k is a zero of the given polynomial function.
-$k = - 1 - 3 i ; f ( x ) = x ^ { 2 } - 2 x + 10$

Accepted Answer

A) True 
 B)False

Question 2

Find a polynomial of least degree with only real coefficients and having the given zeros.
-$1 - \sqrt { 3 } , 1 + \sqrt { 3 }$, and $1 + i$

Accepted Answer

A)  $f ( x ) = x ^ { 4 } + 3 x ^ { 3 } + 4 x ^ { 2 } - 1$ 
B)  $f ( x ) = x ^ { 4 } - 6 x ^ { 3 } + 8 x ^ { 2 } - 4$ 
C)  $f ( x ) = x ^ { 4 } - 4 x ^ { 3 } + 4 x ^ { 2 } - 4$ 
D)  $f ( x ) = x ^ { 4 } + 6 x ^ { 3 } + 4 x ^ { 2 } - 4$ 
A)  $f ( x ) = x ^ { 4 } + 3 x ^ { 3 } + 4 x ^ { 2 } - 1$ 
B)  $f ( x ) = x ^ { 4 } - 6 x ^ { 3 } + 8 x ^ { 2 } - 4$ 
C)  $f ( x ) = x ^ { 4 } - 4 x ^ { 3 } + 4 x ^ { 2 } - 4$ 
D)  $f ( x ) = x ^ { 4 } + 6 x ^ { 3 } + 4 x ^ { 2 } - 4$

Question 3

Find the equation that the given graph represents.
-

Accepted Answer

A)  $P ( x ) = - x ^ { 5 } - 20 x ^ { 4 } - 100 x ^ { 2 } + 100 x$ 
B)  $P ( x ) = x ^ { 5 } - 10 x ^ { 4 } - 100 x ^ { 2 } + 100$ 
C)  $P ( x ) = - x ^ { 6 } + 10 x ^ { 4 } - 100 x ^ { 2 } - 100$ 
D)  $P ( x ) = - x ^ { 6 } + 20 x ^ { 4 } - 100 x ^ { 2 } + 100$ 
A)  $P ( x ) = - x ^ { 5 } - 20 x ^ { 4 } - 100 x ^ { 2 } + 100 x$ 
B)  $P ( x ) = x ^ { 5 } - 10 x ^ { 4 } - 100 x ^ { 2 } + 100$ 
C)  $P ( x ) = - x ^ { 6 } + 10 x ^ { 4 } - 100 x ^ { 2 } - 100$ 
D)  $P ( x ) = - x ^ { 6 } + 20 x ^ { 4 } - 100 x ^ { 2 } + 100$

Question 4

$$x \text { varies inversely as } v \text {, and } x = 45 \text { when } v = 5 \text {. Find } x \text { when } v = 25 \text {. }$$

Accepted Answer

A)  25 
B)  5 
C)  45 
D)  9 
A)  25 
B)  5 
C)  45 
D)  9

Question 5

Find an equation for the rational function graph.
-

Accepted Answer

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

Question 6

Sketch the graph of the polynomial function.
-$$f ( x ) = - \frac { 1 } { 4 } x ^ { 2 }$$

Accepted Answer

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

Question 7

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 8

Give the equation of any oblique asymptotes.
-$$f ( x ) = \frac { 2 x ^ { 2 } } { 3 x ^ { 2 } + 8 }$$

Accepted Answer

A)  $x = y + 2$ 
B)  none 
C)  $y = x + 2$ 
D)  $y = x + \frac { 2 } { 3 }$ 
A)  $x = y + 2$ 
B)  none 
C)  $y = x + 2$ 
D)  $y = x + \frac { 2 } { 3 }$

Question 9

Round to the nearest tenth unless indicated otherwise.
-The volume of wood in a tree varies jointly as the height of the tree and the square of the distance around the tree trunk. If the volume of wood is 15.84 cubic feet when the height is 22 feet and the distance around the trunk
Is 3 feet, what is the volume of wood obtained from a tree that is 23 feet tall having a measurement of 4 feet
Around the trunk?

Accepted Answer

A)  $33.4 \mathrm { ft } ^ { 3 }$ 
B)  $21.4 \mathrm { ft } ^ { 3 }$ 
C)  $29.4 \mathrm { ft } ^ { 3 }$ 
D)  $38.4 \mathrm { ft } ^ { 3 }$ 
A)  $33.4 \mathrm { ft } ^ { 3 }$ 
B)  $21.4 \mathrm { ft } ^ { 3 }$ 
C)  $29.4 \mathrm { ft } ^ { 3 }$ 
D)  $38.4 \mathrm { ft } ^ { 3 }$

Question 10

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions.
-Zeros of $- 3 , - 1,4$ and $P ( 2 ) = 5$

Accepted Answer

A)  $P ( x ) = \frac { x ^ { 3 } } { 6 } + \frac { 19 x } { 6 } - 2$ 
B)  $P ( x ) = \frac { x ^ { 3 } } { 6 } - \frac { 13 x } { 6 } - 2$ 
C)  $P ( x ) = - \frac { x ^ { 3 } } { 6 } - \frac { 19 x } { 6 } - 2$ 
D)  $P ( x ) = - \frac { x ^ { 3 } } { 6 } + \frac { 13 x } { 6 } + 2$ 
A)  $P ( x ) = \frac { x ^ { 3 } } { 6 } + \frac { 19 x } { 6 } - 2$ 
B)  $P ( x ) = \frac { x ^ { 3 } } { 6 } - \frac { 13 x } { 6 } - 2$ 
C)  $P ( x ) = - \frac { x ^ { 3 } } { 6 } - \frac { 19 x } { 6 } - 2$ 
D)  $P ( x ) = - \frac { x ^ { 3 } } { 6 } + \frac { 13 x } { 6 } + 2$

Question 11

Use a graphing calculator to approximate the real zeros. Give each zero as a decimal to the nearest tenth.
-$f ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 11 x - 22$

Accepted Answer

A)  $2,3.2 , - 3.2$ 
B)  $- 2,3.3 , - 3.3$ 
C)  $2,3.3 , - 3.3$ 
D)  $- 2,3.4 , - 3.4$ 
A)  $2,3.2 , - 3.2$ 
B)  $- 2,3.3 , - 3.3$ 
C)  $2,3.3 , - 3.3$ 
D)  $- 2,3.4 , - 3.4$

Question 12

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

Question 13

Determine whether the statement is true or false.
-$$\text { The function } f ( x ) = \frac { 1 } { x } \text { is decreasing on the interval } ( 0 , \infty )$$

Accepted Answer

A) True 
 B)False

Question 14

Determine which of the rational functions given below has the following feature(s).
-The x-intercept is (2, 0)

Accepted Answer

A)  $f ( x ) = \frac { x + 9 } { x - 2 }$ 
B)  $f ( x ) = \frac { 2 x - 1 } { x + 9 }$ 
C)  $f ( x ) = \frac { x - 2 } { x + 9 }$ 
D)  $f ( x ) = \frac { x + 2 } { x + 9 }$ 
A)  $f ( x ) = \frac { x + 9 } { x - 2 }$ 
B)  $f ( x ) = \frac { 2 x - 1 } { x + 9 }$ 
C)  $f ( x ) = \frac { x - 2 } { x + 9 }$ 
D)  $f ( x ) = \frac { x + 2 } { x + 9 }$

Question 15

A rock is propelled upward from the top of a building 170 feet tall at an initial velocity of 168 feet per second. The function that describes the height of the rocket in terms of time t is $s ( t ) = - 16 t ^ { 2 } + 168 t + 170$ Determine the
Maximum height that the rock reaches.

Accepted Answer

A)  630 ft 
B)  592 ft 
C)  579 ft 
D)  611 ft 
A)  630 ft 
B)  592 ft 
C)  579 ft 
D)  611 ft

Question 16

Sketch the graph of the polynomial function.
-$$f ( x ) = \frac { 1 } { 3 } ( x + 2 ) ^ { 4 } + 3$$

Accepted Answer

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

Question 17

Give all possible rational zeros for the following polynomial.
-$$P ( x ) = 2 x ^ { 3 } - 5 x ^ { 2 } + 7 x - 17$$

Accepted Answer

A)  $\pm 1 , \pm 2 , \pm 17$ 
B)  $\pm 1 , \pm 2 , \pm 17 , \pm \frac { 17 } { 2 }$ 
C)  $\pm 1 , \pm 17 , \pm \frac { 1 } { 2 } , \pm \frac { 17 } { 2 }$ 
D)  $\pm 1 , \pm \frac { 1 } { 17 } , \pm 2 , \pm \frac { 2 } { 17 }$ 
A)  $\pm 1 , \pm 2 , \pm 17$ 
B)  $\pm 1 , \pm 2 , \pm 17 , \pm \frac { 17 } { 2 }$ 
C)  $\pm 1 , \pm 17 , \pm \frac { 1 } { 2 } , \pm \frac { 17 } { 2 }$ 
D)  $\pm 1 , \pm \frac { 1 } { 17 } , \pm 2 , \pm \frac { 2 } { 17 }$

Question 18

Use a graphing calculator to approximate the real zeros. Give each zero as a decimal to the nearest tenth.
-$$f ( x ) = 2 x ^ { 3 } + x ^ { 2 } - 14 x - 7$$

Accepted Answer

A)  $- 0.5,2.6 , - 2.6$ 
B)  $0.5,2.6 , - 2.6$ 
C)  $- 2,2.7 , - 2.7$ 
D)  $2,7 , - 7$ 
A)  $- 0.5,2.6 , - 2.6$ 
B)  $0.5,2.6 , - 2.6$ 
C)  $- 2,2.7 , - 2.7$ 
D)  $2,7 , - 7$

Question 19

Identify the vertex of the parabola.
-$$f ( x ) = ( x + 8 ) ^ { 2 }$$

Accepted Answer

A)  $( - 8,0 )$ 
B)  $( 8,0 )$ 
C)  $( 0 , - 8 )$ 
D)  $( 0,8 )$ 
A)  $( - 8,0 )$ 
B)  $( 8,0 )$ 
C)  $( 0 , - 8 )$ 
D)  $( 0,8 )$

Question 20

Identify the vertex of the parabola.
-$$y = x ^ { 2 } + 5$$

Accepted Answer

A)  $( 5,0 )$ 
B)  $( - 5,0 )$ 
C)  $( 0,5 )$ 
D)  $( 0 , - 5 )$ 
A)  $( 5,0 )$ 
B)  $( - 5,0 )$ 
C)  $( 0,5 )$ 
D)  $( 0 , - 5 )$

Use synthetic division to decide whether the given number k is a zero of the given polynomial function. - $k = - 1 - 3 i ; f ( x ) = x ^ { 2 } - 2 x + 10$

Find a polynomial of least degree with only real coefficients and having the given zeros. - $1 - \sqrt { 3 } , 1 + \sqrt { 3 }$ , and $1 + i$

Find the equation that the given graph represents. -

$x \text { varies inversely as } v \text {, and } x = 45 \text { when } v = 5 \text {. Find } x \text { when } v = 25 \text {. }$

Find an equation for the rational function graph. -

Sketch the graph of the polynomial function. - $f ( x ) = - \frac { 1 } { 4 } x ^ { 2 }$ $Sketch the graph of the polynomial function. - f ( x ) = - \frac { 1 } { 4 } x ^ { 2 }$

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

Give the equation of any oblique asymptotes. - $f ( x ) = \frac { 2 x ^ { 2 } } { 3 x ^ { 2 } + 8 }$

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions. -Zeros of $- 3 , - 1,4$ and $P ( 2 ) = 5$

Use a graphing calculator to approximate the real zeros. Give each zero as a decimal to the nearest tenth. - $f ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 11 x - 22$

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?

Determine whether the statement is true or false. - $\text { The function } f ( x ) = \frac { 1 } { x } \text { is decreasing on the interval } ( 0 , \infty )$

Determine which of the rational functions given below has the following feature(s). -The x-intercept is (2, 0)

A rock is propelled upward from the top of a building 170 feet tall at an initial velocity of 168 feet per second. The function that describes the height of the rocket in terms of time t is $s ( t ) = - 16 t ^ { 2 } + 168 t + 170$ Determine the Maximum height that the rock reaches.

Sketch the graph of the polynomial function. - $f ( x ) = \frac { 1 } { 3 } ( x + 2 ) ^ { 4 } + 3$ $Sketch the graph of the polynomial function. - f ( x ) = \frac { 1 } { 3 } ( x + 2 ) ^ { 4 } + 3$

Give all possible rational zeros for the following polynomial. - $P ( x ) = 2 x ^ { 3 } - 5 x ^ { 2 } + 7 x - 17$

Use a graphing calculator to approximate the real zeros. Give each zero as a decimal to the nearest tenth. - $f ( x ) = 2 x ^ { 3 } + x ^ { 2 } - 14 x - 7$

Identify the vertex of the parabola. - $f ( x ) = ( x + 8 ) ^ { 2 }$

Identify the vertex of the parabola. - $y = x ^ { 2 } + 5$

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Inverse, Exponential, and Logarithmic Functions

Systems and Matrices

Arithmetic Sequence: Common Difference and First n Terms

Filters

Exam 4: Polynomials and Rational Functions

Use synthetic division to decide whether the given number k is a zero of the given polynomial function. - k=−1−3i;f(x)=x2−2x+10k = - 1 - 3 i ; f ( x ) = x ^ { 2 } - 2 x + 10k=−1−3i;f(x)=x2−2x+10

Find a polynomial of least degree with only real coefficients and having the given zeros. - 1−3,1+31 - \sqrt { 3 } , 1 + \sqrt { 3 }1−3​,1+3​ , and 1+i1 + i1+i

Find the equation that the given graph represents. -

x varies inversely as v, and x=45 when v=5. Find x when v=25. x \text { varies inversely as } v \text {, and } x = 45 \text { when } v = 5 \text {. Find } x \text { when } v = 25 \text {. }x varies inversely as v, and x=45 when v=5. Find x when v=25.

Find an equation for the rational function graph. -

Sketch the graph of the polynomial function. - f(x)=−14x2f ( x ) = - \frac { 1 } { 4 } x ^ { 2 }f(x)=−41​x2

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

Give the equation of any oblique asymptotes. - f(x)=2x23x2+8f ( x ) = \frac { 2 x ^ { 2 } } { 3 x ^ { 2 } + 8 }f(x)=3x2+82x2​

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions. -Zeros of −3,−1,4- 3 , - 1,4−3,−1,4 and P(2)=5P ( 2 ) = 5P(2)=5

Use a graphing calculator to approximate the real zeros. Give each zero as a decimal to the nearest tenth. - f(x)=x3+2x2−11x−22f ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 11 x - 22f(x)=x3+2x2−11x−22

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?

Determine whether the statement is true or false. - The function f(x)=1x is decreasing on the interval (0,∞)\text { The function } f ( x ) = \frac { 1 } { x } \text { is decreasing on the interval } ( 0 , \infty ) The function f(x)=x1​ is decreasing on the interval (0,∞)

Determine which of the rational functions given below has the following feature(s). -The x-intercept is (2, 0)

Sketch the graph of the polynomial function. - f(x)=13(x+2)4+3f ( x ) = \frac { 1 } { 3 } ( x + 2 ) ^ { 4 } + 3f(x)=31​(x+2)4+3

Give all possible rational zeros for the following polynomial. - P(x)=2x3−5x2+7x−17P ( x ) = 2 x ^ { 3 } - 5 x ^ { 2 } + 7 x - 17P(x)=2x3−5x2+7x−17

Use a graphing calculator to approximate the real zeros. Give each zero as a decimal to the nearest tenth. - f(x)=2x3+x2−14x−7f ( x ) = 2 x ^ { 3 } + x ^ { 2 } - 14 x - 7f(x)=2x3+x2−14x−7

Identify the vertex of the parabola. - f(x)=(x+8)2f ( x ) = ( x + 8 ) ^ { 2 }f(x)=(x+8)2

Identify the vertex of the parabola. - y=x2+5y = x ^ { 2 } + 5y=x2+5

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Inverse, Exponential, and Logarithmic Functions

Systems and Matrices

Arithmetic Sequence: Common Difference and First n Terms

Filters

Use synthetic division to decide whether the given number k is a zero of the given polynomial function. - $k = - 1 - 3 i ; f ( x ) = x ^ { 2 } - 2 x + 10$

Find a polynomial of least degree with only real coefficients and having the given zeros. - $1 - \sqrt { 3 } , 1 + \sqrt { 3 }$ , and $1 + i$

$x \text { varies inversely as } v \text {, and } x = 45 \text { when } v = 5 \text {. Find } x \text { when } v = 25 \text {. }$

Sketch the graph of the polynomial function. - $f ( x ) = - \frac { 1 } { 4 } x ^ { 2 }$ $Sketch the graph of the polynomial function. - f ( x ) = - \frac { 1 } { 4 } x ^ { 2 }$

Give the equation of any oblique asymptotes. - $f ( x ) = \frac { 2 x ^ { 2 } } { 3 x ^ { 2 } + 8 }$

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions. -Zeros of $- 3 , - 1,4$ and $P ( 2 ) = 5$

Use a graphing calculator to approximate the real zeros. Give each zero as a decimal to the nearest tenth. - $f ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 11 x - 22$

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?

Determine whether the statement is true or false. - $\text { The function } f ( x ) = \frac { 1 } { x } \text { is decreasing on the interval } ( 0 , \infty )$

Sketch the graph of the polynomial function. - $f ( x ) = \frac { 1 } { 3 } ( x + 2 ) ^ { 4 } + 3$ $Sketch the graph of the polynomial function. - f ( x ) = \frac { 1 } { 3 } ( x + 2 ) ^ { 4 } + 3$

Give all possible rational zeros for the following polynomial. - $P ( x ) = 2 x ^ { 3 } - 5 x ^ { 2 } + 7 x - 17$

Use a graphing calculator to approximate the real zeros. Give each zero as a decimal to the nearest tenth. - $f ( x ) = 2 x ^ { 3 } + x ^ { 2 } - 14 x - 7$

Identify the vertex of the parabola. - $f ( x ) = ( x + 8 ) ^ { 2 }$

Identify the vertex of the parabola. - $y = x ^ { 2 } + 5$