Question 1

Graph the function.
-$$f ( x ) = \frac { 4 } { ( x + 2 ) ^ { 2 } }$$

Accepted Answer

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

Question 2

Tell whether a linear model or a quadratic model is appropriate for the data. If linear, tell whether the slope should be
positive or negative. If quadratic, decide whether the leading coefficient a of $x ^ { 2 }$ should be positive or negative.
-

Accepted Answer

A)  linear; positive 
B)  quadratic; negative 
C)  quadratic; positive 
D)  linear; negative 
A)  linear; positive 
B)  quadratic; negative 
C)  quadratic; positive 
D)  linear; negative

Question 3

Round your answer to two decimal places.
-The distance to the horizon varies directly as the square root of the height above ground level of the observer. If a person can see 6 miles from a height of 25 feet, how far can a person see from a height
Of 49 feet?

Accepted Answer

A)  8.4 mi 
B)  8.7 mi 
C)  9.6 mi 
D)  7.7 mi 
A)  8.4 mi 
B)  8.7 mi 
C)  9.6 mi 
D)  7.7 mi

Question 4

Solve the problem
-$x$ and $y$ are two positive numbers and $y$ is three greater than $x$. The product of the numbers is 340 . Find the smaller number, $x$.

Accepted Answer

A)  9 
B)  17 
C)  20 
D)  10 
A)  9 
B)  17 
C)  20 
D)  10

Question 5

Give the equations of any horizontal asymptotes.
-$$g ( x ) = \frac { x + 8 } { x ^ { 2 } - 8 }$$

Accepted Answer

A)  $y = 1$ 
B)  none 
C)  $y = 8$ 
D)  $y = 0$ 
A)  $y = 1$ 
B)  none 
C)  $y = 8$ 
D)  $y = 0$

Question 6

Give the equations of any horizontal asymptotes.
-$$f ( x ) = \frac { x ^ { 2 } + 5 } { x ^ { 2 } - 5 }$$

Accepted Answer

A)  $y = 5$ 
B)  $y = 1$ 
C)  $y = 0$ 
D)  none 
A)  $y = 5$ 
B)  $y = 1$ 
C)  $y = 0$ 
D)  none

Question 7

Find the zeros of the polynomial function and state the multiplicity of each.
-$$f ( x ) = 3 x ( x - 8 ) ( x + 11 )$$

Accepted Answer

A)  -11 (multiplicity 1), 0 (multiplicity 1), 8 (multiplicity 1) 
B)  -11 (multiplicity 1), 8 (multiplicity 1 ) 
C)  $- 11$ (multiplicity 1) 8 (multiplicity 2) 
D)  -11 (multiplicity 1 ), 11 (multiplicity 1 ), 8 (multiplicity 1 ) 
A)  -11 (multiplicity 1), 0 (multiplicity 1), 8 (multiplicity 1) 
B)  -11 (multiplicity 1), 8 (multiplicity 1 ) 
C)  $- 11$ (multiplicity 1) 8 (multiplicity 2) 
D)  -11 (multiplicity 1 ), 11 (multiplicity 1 ), 8 (multiplicity 1 )

Question 8

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary.
-$$f ( x ) = x ^ { 4 } - 9$$

Accepted Answer

A)  $\sqrt { 3 } , - \sqrt { 3 } , 3 i , - 3 i$ 
B)  $\sqrt { 3 } , - \sqrt { 3 }$ 
C)  $\sqrt { 3 } , \sqrt { 3 } \mathrm { i }$ 
D)  $\sqrt { 3 } , - \sqrt { 3 } i , \sqrt { 3 } i , - \sqrt { 3 }$ 
A)  $\sqrt { 3 } , - \sqrt { 3 } , 3 i , - 3 i$ 
B)  $\sqrt { 3 } , - \sqrt { 3 }$ 
C)  $\sqrt { 3 } , \sqrt { 3 } \mathrm { i }$ 
D)  $\sqrt { 3 } , - \sqrt { 3 } i , \sqrt { 3 } i , - \sqrt { 3 }$

Question 9

Determine whether the statement is true or false.
-If f(x) is a polynomial having only real coefficients and 2 - 4i is a zero of f(x), then 2 + 4i is also a 
zero.

Accepted Answer

A) True 
 B)False

Question 10

Use the boundedness theorem to determine whether the polynomial function satisfies the given condition.
-The polynomial $f ( x ) = x ^ { 5 } + 10 x ^ { 4 } - 25 x ^ { 3 } - 10 x ^ { 2 } + 24 x$ 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 11

Use the boundedness theorem to determine whether the polynomial function satisfies the given condition.
-The polynomial $f ( x ) = x ^ { 5 } - 5 x ^ { 3 } + 4 x$ has no real zero greater than 2 .

Accepted Answer

A)  Yes, the boundedness theorem shows that the polynomial has no real zero greater than 2. 
B)  No, the boundedness theorem does not show that the polynomial has no real zero greater than 2. 
A)  Yes, the boundedness theorem shows that the polynomial has no real zero greater than 2. 
B)  No, the boundedness theorem does not show that the polynomial has no real zero greater than 2.

Question 12

Round your answer to two decimal places.
-The area of a circle varies directly as the square of the radius of the circle. If a circle with a radius of 5 inches has an area of 78.5 square inches, what is the area of a circle with a radius of 8 inches?

Accepted Answer

A)  $50.24 \mathrm { in } ^ { 2 }$ 
B)  $25.12 \mathrm { in } ^ { 2 }$ 
C)  $200.96$ in $^ { 2 }$ 
D)  $203.36$ in $^ { 2 }$ 
A)  $50.24 \mathrm { in } ^ { 2 }$ 
B)  $25.12 \mathrm { in } ^ { 2 }$ 
C)  $200.96$ in $^ { 2 }$ 
D)  $203.36$ in $^ { 2 }$

Question 13

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

Accepted Answer

A)  $x ^ { 2 } - 3 x + 6 + \frac { 6 } { x + 2 }$ 
B)  $x ^ { 2 } - 2 x + 6 + \frac { 6 } { x + 2 }$ 
C)  $x ^ { 2 } + 3 x + 6 + \frac { - 7 } { x + 2 }$ 
D)  $x ^ { 2 } - 3 x + 6 + \frac { - 7 } { x + 2 }$ 
A)  $x ^ { 2 } - 3 x + 6 + \frac { 6 } { x + 2 }$ 
B)  $x ^ { 2 } - 2 x + 6 + \frac { 6 } { x + 2 }$ 
C)  $x ^ { 2 } + 3 x + 6 + \frac { - 7 } { x + 2 }$ 
D)  $x ^ { 2 } - 3 x + 6 + \frac { - 7 } { x + 2 }$

Question 14

Give all possible rational zeros for the following polynomial.
-$$P ( x ) = - 2 x ^ { 4 } + 5 x ^ { 3 } + 6 x ^ { 2 } + 18$$

Accepted Answer

A)  $\pm 1 , \pm 2 , \pm 3 , \pm 6 , \pm 9 , \pm 18$ 
B)  $\pm 1 , \pm \frac { 1 } { 2 } , \pm 2 , \pm 3 , \pm \frac { 3 } { 2 } , \pm 6 , \pm 9 , \pm \frac { 9 } { 2 } , \pm 18$ 
C)  $\pm 1 , \pm \frac { 1 } { 2 } , \pm 2 , \pm 3 , \pm 6 , \pm 9 , \pm 18$ 
D)  $\pm 1 , \pm 2 , \pm \frac { 1 } { 2 } , \pm \frac { 1 } { 3 } , \pm \frac { 1 } { 6 } , \pm \frac { 1 } { 9 } , \pm \frac { 1 } { 18 }$ 
A)  $\pm 1 , \pm 2 , \pm 3 , \pm 6 , \pm 9 , \pm 18$ 
B)  $\pm 1 , \pm \frac { 1 } { 2 } , \pm 2 , \pm 3 , \pm \frac { 3 } { 2 } , \pm 6 , \pm 9 , \pm \frac { 9 } { 2 } , \pm 18$ 
C)  $\pm 1 , \pm \frac { 1 } { 2 } , \pm 2 , \pm 3 , \pm 6 , \pm 9 , \pm 18$ 
D)  $\pm 1 , \pm 2 , \pm \frac { 1 } { 2 } , \pm \frac { 1 } { 3 } , \pm \frac { 1 } { 6 } , \pm \frac { 1 } { 9 } , \pm \frac { 1 } { 18 }$

Question 15

Answer the question
-$$\text { How can the graph of } f ( x ) = \frac { 1 } { x - 5 } \text { be obtained from the graph of } y = \frac { 1 } { x } \text { ? }$$

Accepted Answer

A)  By making a horizontal shift of 5 units to the left 
B)  By making a vertical shift of 5 units down 
C)  By making a horizontal shift of 5 units to the right 
D)  By making a vertical shift of 5 units up 
A)  By making a horizontal shift of 5 units to the left 
B)  By making a vertical shift of 5 units down 
C)  By making a horizontal shift of 5 units to the right 
D)  By making a vertical shift of 5 units up

Question 16

Tell whether a linear model or a quadratic model is appropriate for the data. If linear, tell whether the slope should be
positive or negative. If quadratic, decide whether the leading coefficient a of $x ^ { 2 }$ should be positive or negative.
-The amount of sales tax paid as a function of the sales price.

Accepted Answer

A)  quadratic; positive 
B)  linear; negative 
C)  quadratic; negative 
D)  linear; positive 
A)  quadratic; positive 
B)  linear; negative 
C)  quadratic; negative 
D)  linear; positive

Question 17

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

Accepted Answer

A)  $\frac { 4 } { 3 }$ (multiplicity 3 $) , \pm 4$ i (multiplicity 2 ) 
B)  $\frac { 2 } { 3 }$ (multiplicity 3), $\pm 4$ i (multiplicity 2 ) 
C)  $- \frac { 2 } { 3 }$ (multiplicity 3 $) , \pm 4$ i (multiplicity 2 ) 
D)  $\frac { 2 } { 3 }$ (multiplicity 3 ), $\pm 4$ (multiplicity 2 ) 
A)  $\frac { 4 } { 3 }$ (multiplicity 3 $) , \pm 4$ i (multiplicity 2 ) 
B)  $\frac { 2 } { 3 }$ (multiplicity 3), $\pm 4$ i (multiplicity 2 ) 
C)  $- \frac { 2 } { 3 }$ (multiplicity 3 $) , \pm 4$ i (multiplicity 2 ) 
D)  $\frac { 2 } { 3 }$ (multiplicity 3 ), $\pm 4$ (multiplicity 2 )

Question 18

Find an equation for the rational function graph.
-If the average cost per unit $C ( x )$ to produce $x$ units of plywood is given by $C ( x ) = \frac { 900 } { x + 30 }$, what is th unit cost for 50 units?

Accepted Answer

A)  $\$ 18.00$ 
B)  $- \$ 12.00$ 
C)  $\$ 11.25$ 
D)  $\$ 0.60$ 
A)  $\$ 18.00$ 
B)  $- \$ 12.00$ 
C)  $\$ 11.25$ 
D)  $\$ 0.60$

Question 19

Solve.
-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. $$\begin{array} { c | c } 
\text { Year, } \mathrm { t } & \text { Population, } \mathrm { P } \
\hline 0 & 59,000 \
\hline 1 & 48,000 \
\hline 2 & 43,500 \
\hline 3 & 49,000 \
\hline 4 & 41,500 \
\hline 5 & 39,000 \
\hline 6 & 42,500
\end{array}$$

Accepted Answer

A)  48,431 
B)  119,000 
C)  81,020 
D)  58,964 
A)  48,431 
B)  119,000 
C)  81,020 
D)  58,964

Question 20

Answer the question
-$$\text { How can the graph of } f ( x ) = - \frac { 1 } { x } - 9 \text { be obtained from the graph of } y = \frac { 1 } { x } \text { ? }$$

Accepted Answer

A)  By reflecting across the x-axis and making a vertical shift of 9 units down 
B)  By making a horizontal shift of 9 units to the left and a vertical shift of 1 unit down 
C)  By reflecting across the y-axis and making a horizontal shift of 9 units to the left 
D)  By making a horizontal shift of 1 unit to the right and a vertical shift of 9 units up 
A)  By reflecting across the x-axis and making a vertical shift of 9 units down 
B)  By making a horizontal shift of 9 units to the left and a vertical shift of 1 unit down 
C)  By reflecting across the y-axis and making a horizontal shift of 9 units to the left 
D)  By making a horizontal shift of 1 unit to the right and a vertical shift of 9 units up

Graph the function. - $f ( x ) = \frac { 4 } { ( x + 2 ) ^ { 2 } }$ $Graph the function. - f ( x ) = \frac { 4 } { ( x + 2 ) ^ { 2 } }$

Round your answer to two decimal places. -The distance to the horizon varies directly as the square root of the height above ground level of the observer. If a person can see 6 miles from a height of 25 feet, how far can a person see from a height Of 49 feet?

Solve the problem - $x$ and $y$ are two positive numbers and $y$ is three greater than $x$ . The product of the numbers is 340 . Find the smaller number, $x$ .

Give the equations of any horizontal asymptotes. - $g ( x ) = \frac { x + 8 } { x ^ { 2 } - 8 }$

Give the equations of any horizontal asymptotes. - $f ( x ) = \frac { x ^ { 2 } + 5 } { x ^ { 2 } - 5 }$

Find the zeros of the polynomial function and state the multiplicity of each. - $f ( x ) = 3 x ( x - 8 ) ( x + 11 )$

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary. - $f ( x ) = x ^ { 4 } - 9$

Determine whether the statement is true or false. -If f(x) is a polynomial having only real coefficients and 2 - 4i is a zero of f(x), then 2 + 4i is also a zero.

Use the boundedness theorem to determine whether the polynomial function satisfies the given condition. -The polynomial $f ( x ) = x ^ { 5 } + 10 x ^ { 4 } - 25 x ^ { 3 } - 10 x ^ { 2 } + 24 x$ has no real zero greater than 3 .

Use the boundedness theorem to determine whether the polynomial function satisfies the given condition. -The polynomial $f ( x ) = x ^ { 5 } - 5 x ^ { 3 } + 4 x$ has no real zero greater than 2 .

Round your answer to two decimal places. -The area of a circle varies directly as the square of the radius of the circle. If a circle with a radius of 5 inches has an area of 78.5 square inches, what is the area of a circle with a radius of 8 inches?

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

Give all possible rational zeros for the following polynomial. - $P ( x ) = - 2 x ^ { 4 } + 5 x ^ { 3 } + 6 x ^ { 2 } + 18$

Answer the question - $\text { How can the graph of } f ( x ) = \frac { 1 } { x - 5 } \text { be obtained from the graph of } y = \frac { 1 } { x } \text { ? }$

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

Find an equation for the rational function graph. -If the average cost per unit $C ( x )$ to produce $x$ units of plywood is given by $C ( x ) = \frac { 900 } { x + 30 }$ , what is th unit cost for 50 units?

Answer the question - $\text { How can the graph of } f ( x ) = - \frac { 1 } { x } - 9 \text { be obtained from the graph of } y = \frac { 1 } { x } \text { ? }$

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

Graph the function. - f(x)=4(x+2)2f ( x ) = \frac { 4 } { ( x + 2 ) ^ { 2 } }f(x)=(x+2)24​

Tell whether a linear model or a quadratic model is appropriate for the data. If linear, tell whether the slope should be positive or negative. If quadratic, decide whether the leading coefficient a of x2x ^ { 2 }x2 should be positive or negative. -