Question 1

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

Accepted Answer

A)  $y = x + 8$ 
B)  $y = x + 4$ 
C)  none 
D)  $x = y + 8$ 
A)  $y = x + 8$ 
B)  $y = x + 4$ 
C)  none 
D)  $x = y + 8$ A

Question 2

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

Accepted Answer

A) True 
 B)False  True

Question 3

Use the equation and the corresponding graph for the quadratic function to find what is requested.
-$f(x)=-2(x-4)^{2}+1$

Find the equation of the axis.

Accepted Answer

A)  $x = 1$ 
B)  $x = 4$ 
C)  $y = 1$ 
D)  $y = 4$ 
A)  $x = 1$ 
B)  $x = 4$ 
C)  $y = 1$ 
D)  $y = 4$ B

Question 4

Suppose z varies directly as the square of x and inversely as y. If x is halved and y is tripled, what happens to z?

Accepted Answer

A)  z is one-sixth as large as before 
B)  z is six times as large as before 
C)  z is multiplied by $\frac { 3 } { 2 }$ 
D)  z is one-twelfth as large as before 
A)  z is one-sixth as large as before 
B)  z is six times as large as before 
C)  z is multiplied by $\frac { 3 } { 2 }$ 
D)  z is one-twelfth as large as before

Question 5

For the polynomial, one zero is given. Find all others.
$P ( x ) = x ^ { 3 } + 5 x ^ { 2 } - 12 x + 14 ; 1 + i$

Accepted Answer

A)   -7,7 
B)   1-i, 7i 
C)   1-i, 7 
D)   1-i,-7 
A)   -7,7 
B)   1-i, 7i 
C)   1-i, 7 
D)   1-i,-7

Question 6

Use synthetic division $$f ( x ) \text { by } x - k \text { for the given value of } k \text {. Then express } f ( x ) \text { in the form } f ( x ) = ( x - k ) q ( x ) + r$$ for the given value of k.
-$f ( x ) = - 5 x ^ { 4 } + x ^ { 3 } + 2 x ^ { 2 } + 3 x - 1 ; k = 1$

Accepted Answer

A)  $f ( x ) = ( x - 1 ) \left( - 5 x ^ { 3 } + 4 x ^ { 2 } - 2 x - 1 \right)$ 
B)  $f ( x ) = ( x - 1 ) \left( - 5 x ^ { 3 } - 4 x ^ { 2 } - 2 x + 1 \right)$ 
C)  $f ( x ) = ( x - 1 ) \left( - 5 x ^ { 3 } + 6 x ^ { 2 } - 4 x - 1 \right)$ 
D)  $f ( x ) = ( x - 1 ) \left( - 5 x ^ { 3 } + 4 x ^ { 2 } + 6 x + 9 \right)$ 
A)  $f ( x ) = ( x - 1 ) \left( - 5 x ^ { 3 } + 4 x ^ { 2 } - 2 x - 1 \right)$ 
B)  $f ( x ) = ( x - 1 ) \left( - 5 x ^ { 3 } - 4 x ^ { 2 } - 2 x + 1 \right)$ 
C)  $f ( x ) = ( x - 1 ) \left( - 5 x ^ { 3 } + 6 x ^ { 2 } - 4 x - 1 \right)$ 
D)  $f ( x ) = ( x - 1 ) \left( - 5 x ^ { 3 } + 4 x ^ { 2 } + 6 x + 9 \right)$

Question 7

Identify the vertex of the parabola.
-$$y = 6 x ^ { 2 } - 72 x + 217$$

Accepted Answer

A)  (1, 6) 
B)  (1, 0) 
C)  (6, 1) 
D)  (6, 0) 
A)  (1, 6) 
B)  (1, 0) 
C)  (6, 1) 
D)  (6, 0)

Question 8

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

Accepted Answer

Rate varies directly

Question 9

The pitch P of a musical tone varies inversely as its wavelength W. One tone has a pitch of 254 vibrations per second and a wavelength of 19.2 ft. Find the wavelength of another tone that has a pitch of 358 vibrations per
Second. Round to the nearest tenth.

Accepted Answer

A)  0 ft 
B)  0.1 ft 
C)  13.6 ft 
D)  4736 ft 
A)  0 ft 
B)  0.1 ft 
C)  13.6 ft 
D)  4736 ft

Question 10

Find all rational zeros and factor f(x).
$f ( x ) = 10 x ^ { 3 } + 33 x ^ { 2 } + 8 x - 3$

Accepted Answer

A) $- 2,5 , - 3 ; f ( x ) = ( x + 2 ) ( x - 5 ) ( x + 3 )$ 
B)  $- 2,5 , - 3 ; f ( x ) = ( 2 x + 1 ) ( 5 x - 1 ) ( x + 3 )$ 
C)  $- \frac { 1 } { 10 } , 1 , - 3 ; f ( x ) = ( 10 x + 1 ) ( x - 1 ) ( x + 3 )$ 
D)  $- \frac { 1 } { 2 } , \frac { 1 } { 5 } , - 3 ; f ( x ) = ( 2 x + 1 ) ( 5 x - 1 ) ( x + 3 )$ 
A) $- 2,5 , - 3 ; f ( x ) = ( x + 2 ) ( x - 5 ) ( x + 3 )$ 
B)  $- 2,5 , - 3 ; f ( x ) = ( 2 x + 1 ) ( 5 x - 1 ) ( x + 3 )$ 
C)  $- \frac { 1 } { 10 } , 1 , - 3 ; f ( x ) = ( 10 x + 1 ) ( x - 1 ) ( x + 3 )$ 
D)  $- \frac { 1 } { 2 } , \frac { 1 } { 5 } , - 3 ; f ( x ) = ( 2 x + 1 ) ( 5 x - 1 ) ( x + 3 )$

Question 11

Use synthetic division $$f ( x ) \text { by } x - k \text { for the given value of } k \text {. Then express } f ( x ) \text { in the form } f ( x ) = ( x - k ) q ( x ) + r$$ for the given value of k.
-$f ( x ) = 3 x ^ { 5 } + 4 x ^ { 4 } + 2 x ^ { 2 } - 1 ; \quad k = - 2$

Accepted Answer

A)  $f ( x ) = ( x + 2 ) \left( 3 x ^ { 4 } - 2 x ^ { 3 } + 6 x ^ { 2 } - 12 \right) + 23$ 
B)  $f ( x ) = ( x + 2 ) \left( 3 x ^ { 4 } - 2 x ^ { 3 } + 4 x ^ { 2 } - 6 x + 12 \right) - 25$ 
C)  $f ( x ) = ( x + 2 ) \left( 3 x ^ { 4 } - 2 x ^ { 3 } + 4 x ^ { 2 } + 6 \right) - 13$ 
D)  $f ( x ) = ( x + 2 ) \left( 3 x ^ { 4 } + 2 x ^ { 3 } + 4 x ^ { 2 } + 8 x \right) - 15$ 
A)  $f ( x ) = ( x + 2 ) \left( 3 x ^ { 4 } - 2 x ^ { 3 } + 6 x ^ { 2 } - 12 \right) + 23$ 
B)  $f ( x ) = ( x + 2 ) \left( 3 x ^ { 4 } - 2 x ^ { 3 } + 4 x ^ { 2 } - 6 x + 12 \right) - 25$ 
C)  $f ( x ) = ( x + 2 ) \left( 3 x ^ { 4 } - 2 x ^ { 3 } + 4 x ^ { 2 } + 6 \right) - 13$ 
D)  $f ( x ) = ( x + 2 ) \left( 3 x ^ { 4 } + 2 x ^ { 3 } + 4 x ^ { 2 } + 8 x \right) - 15$

Question 12

Use the graph to answer the question.
-Find the domain and range of the rational function graphed below.

Accepted Answer

A)  Domain: $( - \infty , 2 ) \cup ( 2 , \infty )$; Range: $( - \infty , \infty )$ 
B)  Domain: $( - \infty , 2 ) \cup ( 2 , \infty )$; Range: $( 1 , \infty )$ 
C)  Domain: $( - \infty , 2 ) \cup ( 2 , \infty )$; Range: $( 0 , \infty )$ 
D)  Domain: $( 2 , \infty )$; Range: $( 0 , \infty )$ 
A)  Domain: $( - \infty , 2 ) \cup ( 2 , \infty )$; Range: $( - \infty , \infty )$ 
B)  Domain: $( - \infty , 2 ) \cup ( 2 , \infty )$; Range: $( 1 , \infty )$ 
C)  Domain: $( - \infty , 2 ) \cup ( 2 , \infty )$; Range: $( 0 , \infty )$ 
D)  Domain: $( 2 , \infty )$; Range: $( 0 , \infty )$

Question 13

A piece of rectangular sheet metal is 21 inches wide. It is to be made into a rain gutter by turning up equal edges to form parallel sides. Let x represent the length of each of the parallel sides. For what value of x will the area of
The cross section be a maximum (and thus maximize the amount of water that the gutter will hold)? If necessary,
Round to 2 decimal places.

Accepted Answer

A)  42 in. 
B)  84 in. 
C)  10.5 in. 
D)  5.25 in. 
A)  42 in. 
B)  84 in. 
C)  10.5 in. 
D)  5.25 in.

Question 14

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

Question 15

How can the graph of $f ( x ) = - \frac { 1 } { x } - 4$ be obtained from the graph of $y = \frac { 1 } { x }$ ?

Accepted Answer

A)  By making a horizontal shift of 4 units to the left and a vertical shift of 1 unit down 
B)  By reflecting across the $x$-axis and making a vertical shift of 4 units down 
C)  By reflecting across the $y$-axis and making a horizontal shift of 4 units to the left 
D)  By making a horizontal shift of 1 unit to the right and a vertical shift of 4 units up 
A)  By making a horizontal shift of 4 units to the left and a vertical shift of 1 unit down 
B)  By reflecting across the $x$-axis and making a vertical shift of 4 units down 
C)  By reflecting across the $y$-axis and making a horizontal shift of 4 units to the left 
D)  By making a horizontal shift of 1 unit to the right and a vertical shift of 4 units up

Question 16

Give the equations of any vertical asymptotes.
-$$f ( x ) = \frac { x - 4 } { x ^ { 2 } + 2 x }$$

Accepted Answer

A)  $x = 4$ 
B)  $x = 2$ 
C)  $x = 0 , x = - 2$ 
D)  $x = - 2$ 
A)  $x = 4$ 
B)  $x = 2$ 
C)  $x = 0 , x = - 2$ 
D)  $x = - 2$

Question 17

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

Accepted Answer

The circumference of

Question 18

Sketch the graph of the rational function.
-$$f ( x ) = \frac { x ^ { 2 } - x - 12 } { x + 4 }$$

Accepted Answer

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

Question 19

The weight of a body above the surface of the earth is inversely proportional to the square of its distance from the center of the earth. What is the effect on the weight when the distance is multiplied by 2?

Accepted Answer

A)  The weight is divided by 2. 
B)  The weight is multiplied by 4. 
C)  The weight is divided by 4. 
D)  The weight is multiplied by 2. 
A)  The weight is divided by 2. 
B)  The weight is multiplied by 4. 
C)  The weight is divided by 4. 
D)  The weight is multiplied by 2.

Question 20

Use synthetic division $$f ( x ) \text { by } x - k \text { for the given value of } k \text {. Then express } f ( x ) \text { in the form } f ( x ) = ( x - k ) q ( x ) + r$$ for the given value of k.
-$f ( x ) = 3 x ^ { 4 } - 2 x ^ { 3 } - 10 x ^ { 2 } + 15 ; \quad k = 2$

Accepted Answer

A)  $f ( x ) = ( x - 2 ) \left( 3 x ^ { 3 } - 4 x ^ { 2 } - 2 x - 4 \right) + 7$ 
B)  $f ( x ) = ( x - 2 ) \left( 3 x ^ { 3 } + 4 x ^ { 2 } + 2 x + 4 \right) + 22$ 
C)  $f ( x ) = ( x - 2 ) \left( 3 x ^ { 3 } + 4 x ^ { 2 } - 2 x - 4 \right) + 7$ 
D)  $f ( x ) = ( x - 2 ) \left( 3 x ^ { 3 } + 4 x ^ { 2 } - 2 x + 11 \right) + 22$ 
A)  $f ( x ) = ( x - 2 ) \left( 3 x ^ { 3 } - 4 x ^ { 2 } - 2 x - 4 \right) + 7$ 
B)  $f ( x ) = ( x - 2 ) \left( 3 x ^ { 3 } + 4 x ^ { 2 } + 2 x + 4 \right) + 22$ 
C)  $f ( x ) = ( x - 2 ) \left( 3 x ^ { 3 } + 4 x ^ { 2 } - 2 x - 4 \right) + 7$ 
D)  $f ( x ) = ( x - 2 ) \left( 3 x ^ { 3 } + 4 x ^ { 2 } - 2 x + 11 \right) + 22$

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

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

Suppose z varies directly as the square of x and inversely as y. If x is halved and y is tripled, what happens to z?

For the polynomial, one zero is given. Find all others. $P ( x ) = x ^ { 3 } + 5 x ^ { 2 } - 12 x + 14 ; 1 + i$

Use synthetic division $f ( x ) \text { by } x - k \text { for the given value of } k \text {. Then express } f ( x ) \text { in the form } f ( x ) = ( x - k ) q ( x ) + r$ for the given value of k. - $f ( x ) = - 5 x ^ { 4 } + x ^ { 3 } + 2 x ^ { 2 } + 3 x - 1 ; k = 1$

Identify the vertex of the parabola. - $y = 6 x ^ { 2 } - 72 x + 217$

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

The pitch P of a musical tone varies inversely as its wavelength W. One tone has a pitch of 254 vibrations per second and a wavelength of 19.2 ft. Find the wavelength of another tone that has a pitch of 358 vibrations per Second. Round to the nearest tenth.

Find all rational zeros and factor f(x). $f ( x ) = 10 x ^ { 3 } + 33 x ^ { 2 } + 8 x - 3$

Use synthetic division $f ( x ) \text { by } x - k \text { for the given value of } k \text {. Then express } f ( x ) \text { in the form } f ( x ) = ( x - k ) q ( x ) + r$ for the given value of k. - $f ( x ) = 3 x ^ { 5 } + 4 x ^ { 4 } + 2 x ^ { 2 } - 1 ; \quad k = - 2$

Use the graph to answer the question. -Find the domain and range of the rational function graphed below.

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?

How can the graph of $f ( x ) = - \frac { 1 } { x } - 4$ be obtained from the graph of $y = \frac { 1 } { x }$ ?

Give the equations of any vertical asymptotes. - $f ( x ) = \frac { x - 4 } { x ^ { 2 } + 2 x }$

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

Sketch the graph of the rational function. - $f ( x ) = \frac { x ^ { 2 } - x - 12 } { x + 4 }$ $Sketch the graph of the rational function. - f ( x ) = \frac { x ^ { 2 } - x - 12 } { x + 4 }$

The weight of a body above the surface of the earth is inversely proportional to the square of its distance from the center of the earth. What is the effect on the weight when the distance is multiplied by 2?

Use synthetic division $f ( x ) \text { by } x - k \text { for the given value of } k \text {. Then express } f ( x ) \text { in the form } f ( x ) = ( x - k ) q ( x ) + r$ for the given value of k. - $f ( x ) = 3 x ^ { 4 } - 2 x ^ { 3 } - 10 x ^ { 2 } + 15 ; \quad k = 2$

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

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

Use the equation and the corresponding graph for the quadratic function to find what is requested. - f(x)=−2(x−4)2+1f(x)=-2(x-4)^{2}+1f(x)=−2(x−4)2+1 Find the equation of the axis.

Suppose z varies directly as the square of x and inversely as y. If x is halved and y is tripled, what happens to z?

For the polynomial, one zero is given. Find all others. P(x)=x3+5x2−12x+14;1+iP ( x ) = x ^ { 3 } + 5 x ^ { 2 } - 12 x + 14 ; 1 + iP(x)=x3+5x2−12x+14;1+i

Identify the vertex of the parabola. - y=6x2−72x+217y = 6 x ^ { 2 } - 72 x + 217y=6x2−72x+217

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

The pitch P of a musical tone varies inversely as its wavelength W. One tone has a pitch of 254 vibrations per second and a wavelength of 19.2 ft. Find the wavelength of another tone that has a pitch of 358 vibrations per Second. Round to the nearest tenth.

Find all rational zeros and factor f(x). f(x)=10x3+33x2+8x−3f ( x ) = 10 x ^ { 3 } + 33 x ^ { 2 } + 8 x - 3f(x)=10x3+33x2+8x−3

Use the graph to answer the question. -Find the domain and range of the rational function graphed below.

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?

How can the graph of f(x)=−1x−4f ( x ) = - \frac { 1 } { x } - 4f(x)=−x1​−4 be obtained from the graph of y=1xy = \frac { 1 } { x }y=x1​ ?

Give the equations of any vertical asymptotes. - f(x)=x−4x2+2xf ( x ) = \frac { x - 4 } { x ^ { 2 } + 2 x }f(x)=x2+2xx−4​

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

Sketch the graph of the rational function. - f(x)=x2−x−12x+4f ( x ) = \frac { x ^ { 2 } - x - 12 } { x + 4 }f(x)=x+4x2−x−12​

The weight of a body above the surface of the earth is inversely proportional to the square of its distance from the center of the earth. What is the effect on the weight when the distance is multiplied by 2?

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

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

For the polynomial, one zero is given. Find all others. $P ( x ) = x ^ { 3 } + 5 x ^ { 2 } - 12 x + 14 ; 1 + i$

Identify the vertex of the parabola. - $y = 6 x ^ { 2 } - 72 x + 217$

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

Find all rational zeros and factor f(x). $f ( x ) = 10 x ^ { 3 } + 33 x ^ { 2 } + 8 x - 3$

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?

How can the graph of $f ( x ) = - \frac { 1 } { x } - 4$ be obtained from the graph of $y = \frac { 1 } { x }$ ?

Give the equations of any vertical asymptotes. - $f ( x ) = \frac { x - 4 } { x ^ { 2 } + 2 x }$

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

Sketch the graph of the rational function. - $f ( x ) = \frac { x ^ { 2 } - x - 12 } { x + 4 }$ $Sketch the graph of the rational function. - f ( x ) = \frac { x ^ { 2 } - x - 12 } { x + 4 }$