Question 1

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

Accepted Answer

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

Question 2

Give the domain and range for the rational function. Use interval notation.
-$$f ( x ) = \frac { 4 } { x }$$

Accepted Answer

A)  Domain: $( - \infty , 4 ) \cup ( 4 , \infty )$; Range: $( 0 , \infty )$ 
B)  Domain: $( - \infty , 0 ) \cup ( 0 , \infty )$; Range: $( 0 , \infty )$ 
C)  Domain: $( - \infty , 0 ) \cup ( 0 , \infty )$; Range: $( - \infty , 0 ) \cup ( 0 , \infty )$ 
D)  Domain: $( - \infty , 4 ) \cup ( 4 , \infty )$; Range: $( - \infty , 0 ) \cup ( 0 , \infty )$ 
A)  Domain: $( - \infty , 4 ) \cup ( 4 , \infty )$; Range: $( 0 , \infty )$ 
B)  Domain: $( - \infty , 0 ) \cup ( 0 , \infty )$; Range: $( 0 , \infty )$ 
C)  Domain: $( - \infty , 0 ) \cup ( 0 , \infty )$; Range: $( - \infty , 0 ) \cup ( 0 , \infty )$ 
D)  Domain: $( - \infty , 4 ) \cup ( 4 , \infty )$; Range: $( - \infty , 0 ) \cup ( 0 , \infty )$

Question 3

Provide an appropriate response.
-For what values of a does the quadratic function $f ( x ) = a x ^ { 2 } - 6 x + 3$ have no $x$-intercepts?

Accepted Answer

A) $a > 3$ B) a $> 9$ C) $a < 3$ D) a $< 9$ A) $a > 3$ B) a $> 9$ C) $a < 3$ D) a $< 9$

Question 4

Find a polynomial of least degree with only real coefficients and having the given zeros.
-$- \sqrt { 6 } , \sqrt { 6 }$, and $- 7$ (multiplicity 2 )

Accepted Answer

A)  $f ( x ) = x ^ { 4 } + 14 x ^ { 3 } + 43 x ^ { 2 } - 84 x - 294$ 
B)  $f ( x ) = x ^ { 3 } - 7 x ^ { 2 } - 6 x + 42$ 
C)  $f ( x ) = x ^ { 4 } - 14 x ^ { 3 } - 43 x ^ { 2 } + 84 x + 294$ 
D)  $f ( x ) = x ^ { 3 } + 7 x ^ { 2 } - 6 x - 42$ 
A)  $f ( x ) = x ^ { 4 } + 14 x ^ { 3 } + 43 x ^ { 2 } - 84 x - 294$ 
B)  $f ( x ) = x ^ { 3 } - 7 x ^ { 2 } - 6 x + 42$ 
C)  $f ( x ) = x ^ { 4 } - 14 x ^ { 3 } - 43 x ^ { 2 } + 84 x + 294$ 
D)  $f ( x ) = x ^ { 3 } + 7 x ^ { 2 } - 6 x - 42$

Question 5

Determine whether the statement is true or false.
-If c is a complex number, then $$5 \bar { c } = \overline { 5 c }$$

Accepted Answer

A) True 
 B)False

Question 6

Round your answer to two decimal places.
-The intensity of a radio signal from the radio station varies inversely as the square of the distance from the station. Suppose the the intensity is 8000 units at a distance of 2 miles. What will the
Intensity be at a distance of 13 miles? Round your answer to the nearest unit.

Accepted Answer

A)  215 units 
B)  172 units 
C)  153 units 
D)  189 units 
A)  215 units 
B)  172 units 
C)  153 units 
D)  189 units

Question 7

Use synthetic division to perform the division.
-$$\frac { 2 x ^ { 3 } + x ^ { 2 } - 5 x + 2 } { x + 5 }$$

Accepted Answer

A)  $2 x ^ { 2 } - 9 x + 40 + \frac { - 198 } { x + 5 }$ 
B)  $2 x ^ { 2 } - 9 x - 40 + \frac { - 198 } { x + 5 }$ 
C)  $2 x ^ { 2 } - 9 x - 40$ 
D)  $2 x ^ { 2 } - 9 x + 40$ 
A)  $2 x ^ { 2 } - 9 x + 40 + \frac { - 198 } { x + 5 }$ 
B)  $2 x ^ { 2 } - 9 x - 40 + \frac { - 198 } { x + 5 }$ 
C)  $2 x ^ { 2 } - 9 x - 40$ 
D)  $2 x ^ { 2 } - 9 x + 40$

Question 8

Determine whether the statement is true or false.
-$$\text { The function } f ( x ) = \frac { 2 - x } { x ^ { 2 } } \text { has an oblique asymptote. }$$ 
`

Accepted Answer

A) True 
 B)False

Question 9

Use synthetic division to decide whether the given number k is a zero of the given polynomial function.
-$$k = - \frac { 1 } { 3 } ; f ( x ) = - 3 x ^ { 4 } + 8 x ^ { 3 } + 2 x + 1$$

Accepted Answer

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

Question 10

Use synthetic division to decide whether the given number k is a zero of the given polynomial function.
-$k = - \frac { 2 } { 5 } ; f ( x ) = - 5 x ^ { 4 } + 5 x ^ { 2 } - 2$

Accepted Answer

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

Question 11

Find a polynomial of least degree with only real coefficients and having the given zeros.
-$3 + \sqrt { 6 } , 3 - \sqrt { 6 }$, and 3

Accepted Answer

A)  $f ( x ) = x ^ { 3 } - 9 x ^ { 2 } + 21 x - 9$ 
B)  $f ( x ) = x ^ { 3 } - 11 x ^ { 2 } + 21 x + 9$ 
C)  $f ( x ) = x ^ { 3 } + 9 x ^ { 2 } + 21 x - 9$ 
D)  $f ( x ) = x ^ { 3 } - 11 x ^ { 2 } + 21 x + 11$ 
A)  $f ( x ) = x ^ { 3 } - 9 x ^ { 2 } + 21 x - 9$ 
B)  $f ( x ) = x ^ { 3 } - 11 x ^ { 2 } + 21 x + 9$ 
C)  $f ( x ) = x ^ { 3 } + 9 x ^ { 2 } + 21 x - 9$ 
D)  $f ( x ) = x ^ { 3 } - 11 x ^ { 2 } + 21 x + 11$

Question 12

Use the remainder theorem and synthetic division to find f(k).
-$$k = - 2 ; f ( x ) = x ^ { 6 } - 2 x ^ { 5 } - 3 x ^ { 4 } - 2 x ^ { 3 } + 3 x ^ { 2 } - 4 x - 6$$

Accepted Answer

A)  -66 
B)  -110 
C)  110 
D)  111 
A)  -66 
B)  -110 
C)  110 
D)  111

Question 13

Identify any vertical, horizontal, or oblique asymptotes in the graph of y = f(x). State the domain of f.
-

Accepted Answer

A)  Vertical: $x = 4$; horizontal: $y = \pm 3 ; ( - \infty , 4 ) \cup ( 4 , \infty )$ 
B)  Vertical: $x = \pm 3$; horizontal: $y = 4 ; ( - \infty , - 3 ) \cup ( - 3 , \infty )$ 
C)  Vertical: $x = 4$; horizontal: $y = \pm 3 ; ( - \infty , - 3 ) \cup ( - 3,3 ) \cup ( 3 , \infty )$ 
D)  Vertical: $x = \pm 3$; horizontal: $y = 4 ; ( - \infty , - 3 ) \cup ( - 3,3 ) \cup ( 3 , \infty )$ 
A)  Vertical: $x = 4$; horizontal: $y = \pm 3 ; ( - \infty , 4 ) \cup ( 4 , \infty )$ 
B)  Vertical: $x = \pm 3$; horizontal: $y = 4 ; ( - \infty , - 3 ) \cup ( - 3 , \infty )$ 
C)  Vertical: $x = 4$; horizontal: $y = \pm 3 ; ( - \infty , - 3 ) \cup ( - 3,3 ) \cup ( 3 , \infty )$ 
D)  Vertical: $x = \pm 3$; horizontal: $y = 4 ; ( - \infty , - 3 ) \cup ( - 3,3 ) \cup ( 3 , \infty )$

Question 14

Solve the problem
-The height of a box is 8 inches. The length is three inches more than the width. Find the width if the volume is 432 cubic inches.

Accepted Answer

A)  54 in. 
B)  $8 \mathrm { in }$. 
C)  9 in. 
D)  $6 \mathrm { in }$. 
A)  54 in. 
B)  $8 \mathrm { in }$. 
C)  9 in. 
D)  $6 \mathrm { in }$.

Question 15

Give all possible rational zeros for the following polynomial.
-$$P ( x ) = x ^ { 3 } - 5 x ^ { 2 } + 4 x - 24$$

Accepted Answer

A)  $\pm 1 , \pm 2 , \pm 3 , \pm 4 , \pm 6 , \pm 12 , \pm 24$ 
B)  $\pm 1 , \pm \frac { 1 } { 2 } , \pm 2 , \pm 3 , \pm 4 , \pm 6 , \pm 8 , \pm 12 , \pm 24$ 
C)  $\pm 1 , \pm 2 , \pm 3 , \pm 4 , \pm 24$ 
D)  $\pm 1 , \pm 2 , \pm 3 , \pm 4 , \pm 6 , \pm 8 , \pm 12 , \pm 24$ 
A)  $\pm 1 , \pm 2 , \pm 3 , \pm 4 , \pm 6 , \pm 12 , \pm 24$ 
B)  $\pm 1 , \pm \frac { 1 } { 2 } , \pm 2 , \pm 3 , \pm 4 , \pm 6 , \pm 8 , \pm 12 , \pm 24$ 
C)  $\pm 1 , \pm 2 , \pm 3 , \pm 4 , \pm 24$ 
D)  $\pm 1 , \pm 2 , \pm 3 , \pm 4 , \pm 6 , \pm 8 , \pm 12 , \pm 24$

Question 16

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary.
-$$f ( x ) = x ^ { 4 } - 32 x ^ { 2 } - 144$$

Accepted Answer

A)  $- 2 i , 2 i , 6 i , - 6 i$ 
B)  $- 2 \mathrm { i } , 2 \mathrm { i } , 12 , - 12$ 
C)  $- 2 i , 2 i , 6 , - 6$ 
D)  $- 2 i , 2 i , 12 i , - 12 i$ 
A)  $- 2 i , 2 i , 6 i , - 6 i$ 
B)  $- 2 \mathrm { i } , 2 \mathrm { i } , 12 , - 12$ 
C)  $- 2 i , 2 i , 6 , - 6$ 
D)  $- 2 i , 2 i , 12 i , - 12 i$

Question 17

Find the domain and range of the function.
-$$f ( x ) = - x ^ { 2 } - 6 x - 16$$

Accepted Answer

A)  Domain: $( - \infty , \infty )$; Range: $( - \infty , 3 ]$ 
B)  Domain: $( - \infty , \infty )$; Range: $[ 7 , \infty )$ 
C)  Domain: $( - \infty , - 7 ]$; Range: $[ 3 , \infty )$ 
D)  Domain: $( - \infty , \infty )$; Range: $( - \infty , - 7 ]$ 
A)  Domain: $( - \infty , \infty )$; Range: $( - \infty , 3 ]$ 
B)  Domain: $( - \infty , \infty )$; Range: $[ 7 , \infty )$ 
C)  Domain: $( - \infty , - 7 ]$; Range: $[ 3 , \infty )$ 
D)  Domain: $( - \infty , \infty )$; Range: $( - \infty , - 7 ]$

Question 18

Find an equation for the rational function graph.
-Suppose the cost per ton, $f ( x )$, to build an oil platform of $x$ thousand tons is approximated by $f ( x ) = \frac { 62,500 } { x + 125 }$. What is the cost per ton for $x = 30$ ?

Accepted Answer

A)  $\$ 403.23$ 
B)  $\$ 2083.33$ 
C)  $\$ 1958.33$ 
D)  $\$ 16.67$ 
A)  $\$ 403.23$ 
B)  $\$ 2083.33$ 
C)  $\$ 1958.33$ 
D)  $\$ 16.67$

Question 19

Find the zeros of the polynomial function and state the multiplicity of each.
-$$f ( x ) = 5 x ( x - 7 ) ^ { 3 } \left( x ^ { 2 } - 16 \right)$$

Accepted Answer

A)  0 (multiplicity 1), $- 16$ (multiplicity 2 ), 7 (multiplicity 3 ) 
B)  0 (multiplicity 1), $\pm 4$ (multiplicity 1), 7 (multiplicity 3) 
C)  $\pm 4$ (multiplicity 1), 7 (multiplicity 3 ) 
D)  0 (multiplicity 1 ), $\pm 4$ (multiplicity 2 ), $- 7$ (multiplicity 3 ) 
A)  0 (multiplicity 1), $- 16$ (multiplicity 2 ), 7 (multiplicity 3 ) 
B)  0 (multiplicity 1), $\pm 4$ (multiplicity 1), 7 (multiplicity 3) 
C)  $\pm 4$ (multiplicity 1), 7 (multiplicity 3 ) 
D)  0 (multiplicity 1 ), $\pm 4$ (multiplicity 2 ), $- 7$ (multiplicity 3 )

Question 20

Translate the given formula to an English phrase using the word "varies".
-What type of variation is suggested by the graph?

Accepted Answer

A)  $y$ varies directly as $x$ 
B)  $y$ varies inversely as the square of $x$ 
C)  $y$ varies inversely as $x$ 
D)  $y$ varies directly as the square of $x$ 
A)  $y$ varies directly as $x$ 
B)  $y$ varies inversely as the square of $x$ 
C)  $y$ varies inversely as $x$ 
D)  $y$ varies directly as the square of $x$

2Given 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 domain and range for the rational function. Use interval notation. - $f ( x ) = \frac { 4 } { x }$

Provide an appropriate response. -For what values of a does the quadratic function $f ( x ) = a x ^ { 2 } - 6 x + 3$ have no $x$ -intercepts?

Find a polynomial of least degree with only real coefficients and having the given zeros. - $- \sqrt { 6 } , \sqrt { 6 }$ , and $- 7$ (multiplicity 2 )

Determine whether the statement is true or false. -If c is a complex number, then $5 \bar { c } = \overline { 5 c }$

Use synthetic division to perform the division. - $\frac { 2 x ^ { 3 } + x ^ { 2 } - 5 x + 2 } { x + 5 }$

Determine whether the statement is true or false. - $\text { The function } f ( x ) = \frac { 2 - x } { x ^ { 2 } } \text { has an oblique asymptote. }$ `

Use synthetic division to decide whether the given number k is a zero of the given polynomial function. - $k = - \frac { 1 } { 3 } ; f ( x ) = - 3 x ^ { 4 } + 8 x ^ { 3 } + 2 x + 1$

Use synthetic division to decide whether the given number k is a zero of the given polynomial function. - $k = - \frac { 2 } { 5 } ; f ( x ) = - 5 x ^ { 4 } + 5 x ^ { 2 } - 2$

Find a polynomial of least degree with only real coefficients and having the given zeros. - $3 + \sqrt { 6 } , 3 - \sqrt { 6 }$ , and 3

Use the remainder theorem and synthetic division to find f(k). - $k = - 2 ; f ( x ) = x ^ { 6 } - 2 x ^ { 5 } - 3 x ^ { 4 } - 2 x ^ { 3 } + 3 x ^ { 2 } - 4 x - 6$

Identify any vertical, horizontal, or oblique asymptotes in the graph of y = f(x). State the domain of f. -

Solve the problem -The height of a box is 8 inches. The length is three inches more than the width. Find the width if the volume is 432 cubic inches.

Give all possible rational zeros for the following polynomial. - $P ( x ) = x ^ { 3 } - 5 x ^ { 2 } + 4 x - 24$

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary. - $f ( x ) = x ^ { 4 } - 32 x ^ { 2 } - 144$

Find the domain and range of the function. - $f ( x ) = - x ^ { 2 } - 6 x - 16$

Find an equation for the rational function graph. -Suppose the cost per ton, $f ( x )$ , to build an oil platform of $x$ thousand tons is approximated by $f ( x ) = \frac { 62,500 } { x + 125 }$ . What is the cost per ton for $x = 30$ ?

Find the zeros of the polynomial function and state the multiplicity of each. - $f ( x ) = 5 x ( x - 7 ) ^ { 3 } \left( x ^ { 2 } - 16 \right)$

Translate the given formula to an English phrase using the word "varies". -What type of variation is suggested by the graph?

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

2Given 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 domain and range for the rational function. Use interval notation. - f(x)=4xf ( x ) = \frac { 4 } { x }f(x)=x4​

Provide an appropriate response. -For what values of a does the quadratic function f(x)=ax2−6x+3f ( x ) = a x ^ { 2 } - 6 x + 3f(x)=ax2−6x+3 have no xxx -intercepts?

Find a polynomial of least degree with only real coefficients and having the given zeros. - −6,6- \sqrt { 6 } , \sqrt { 6 }−6​,6​ , and −7- 7−7 (multiplicity 2 )

Determine whether the statement is true or false. -If c is a complex number, then 5cˉ=5c‾5 \bar { c } = \overline { 5 c }5cˉ=5c

Use synthetic division to perform the division. - 2x3+x2−5x+2x+5\frac { 2 x ^ { 3 } + x ^ { 2 } - 5 x + 2 } { x + 5 }x+52x3+x2−5x+2​

Determine whether the statement is true or false. - The function f(x)=2−xx2 has an oblique asymptote. \text { The function } f ( x ) = \frac { 2 - x } { x ^ { 2 } } \text { has an oblique asymptote. } The function f(x)=x22−x​ has an oblique asymptote. `

Use synthetic division to decide whether the given number k is a zero of the given polynomial function. - k=−13;f(x)=−3x4+8x3+2x+1k = - \frac { 1 } { 3 } ; f ( x ) = - 3 x ^ { 4 } + 8 x ^ { 3 } + 2 x + 1k=−31​;f(x)=−3x4+8x3+2x+1

Use synthetic division to decide whether the given number k is a zero of the given polynomial function. - k=−25;f(x)=−5x4+5x2−2k = - \frac { 2 } { 5 } ; f ( x ) = - 5 x ^ { 4 } + 5 x ^ { 2 } - 2k=−52​;f(x)=−5x4+5x2−2

Find a polynomial of least degree with only real coefficients and having the given zeros. - 3+6,3−63 + \sqrt { 6 } , 3 - \sqrt { 6 }3+6​,3−6​ , and 3

Use the remainder theorem and synthetic division to find f(k). - k=−2;f(x)=x6−2x5−3x4−2x3+3x2−4x−6k = - 2 ; f ( x ) = x ^ { 6 } - 2 x ^ { 5 } - 3 x ^ { 4 } - 2 x ^ { 3 } + 3 x ^ { 2 } - 4 x - 6k=−2;f(x)=x6−2x5−3x4−2x3+3x2−4x−6