Question 1

Graph the function.
-$$f ( x ) = x ^ { 2 } + \frac { 9 } { x }$$

Accepted Answer

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

Question 2

Graph the polynomial function.
-$f(x)=4 x^{2}-x^{3}$

Accepted Answer

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

Question 3

Find the x- and y-intercepts of f.
-$$f ( x ) = x ^ { 2 } ( x - 2 ) ( x - 1 )$$

Accepted Answer

A) x-intercepts: 0, -2, -1; y-intercept: 0 
B) x-intercepts: 0, -2, -1; y-intercept: 2 
C) x-intercepts: 0, 2, 1; y-intercept: 2 
D) x-intercepts: 0, 2, 1; y-intercept: 0 
A) x-intercepts: 0, -2, -1; y-intercept: 0 
B) x-intercepts: 0, -2, -1; y-intercept: 2 
C) x-intercepts: 0, 2, 1; y-intercept: 2 
D) x-intercepts: 0, 2, 1; y-intercept: 0

Question 4

Give the equation of the slant asymptote, if any, of the function.
-$$( x ) = \frac { x ^ { 2 } + 5 x - 2 } { x - 7 }$$

Accepted Answer

A) y = x + 12 
B) none 
C) x = y + 12 
D) y = x - 2 
A) y = x + 12 
B) none 
C) x = y + 12 
D) y = x - 2

Question 5

Graph the function.
-$(x)=\frac{x-2}{x^{2}-x-20}$

Accepted Answer

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

Question 6

Use the Factor Theorem to determine whether x - c is a factor of f(x).
-$$f ( x ) = x ^ { 4 } + 11 x ^ { 3 } + 6 x ^ { 2 } + 64 x - 22 ; x + 11$$

Accepted Answer

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

Question 7

Find the axis of symmetry of the quadratic function.
-$$f ( x ) = - 7 ( x - 2 ) ^ { 2 } - 5$$

Accepted Answer

A)  $x = - 2$ 
B)  $x = 2$ 
C)  $x = - 7$ 
D)  $x = - 5$ 
A)  $x = - 2$ 
B)  $x = 2$ 
C)  $x = - 7$ 
D)  $x = - 5$

Question 8

Find the x- and y-intercepts of f.
-$$f ( x ) = - x ^ { 2 } ( x + 6 ) \left( x ^ { 2 } + 1 \right)$$

Accepted Answer

A) x-intercepts: -6, -1, 0; y-intercept: 6 
B) x-intercepts: -6, -1, 0; y-intercept: -6 
C) x-intercepts: -6, 0; y-intercept: 0 
D) x-intercepts: -6, -1, 0, 1; y-intercept: 0 
A) x-intercepts: -6, -1, 0; y-intercept: 6 
B) x-intercepts: -6, -1, 0; y-intercept: -6 
C) x-intercepts: -6, 0; y-intercept: 0 
D) x-intercepts: -6, -1, 0, 1; y-intercept: 0

Question 9

Find the range of the quadratic function in interval notation.
-$$f ( x ) = x ^ { 2 } + 8 x + 6$$

Accepted Answer

A)  $( - \infty , - 42 ]$ 
B)  $[ - 10 , \infty )$ 
C)  $[ 4 , \infty )$ 
D)  $( - \infty , - 10 ]$ 
A)  $( - \infty , - 42 ]$ 
B)  $[ - 10 , \infty )$ 
C)  $[ 4 , \infty )$ 
D)  $( - \infty , - 10 ]$

Question 10

First rewrite the quadratic function in standard form by completing the square, then find any x-intercepts and any y-intercepts.
-$$f ( x ) = x ^ { 2 } + 3 x + 2$$

Accepted Answer

A)  $x$-intercepts: $- 1$ and $2 ; y$-intercept: 2 
B)  x-intercepts: $- 1$ and -2; y-intercept: 2 
C)  x-intercepts: 1 and 2; $y$-intercept: $- 1$ 
D)  $x$-intercepts: 1 and -2; $y$-intercept: 0 
A)  $x$-intercepts: $- 1$ and $2 ; y$-intercept: 2 
B)  x-intercepts: $- 1$ and -2; y-intercept: 2 
C)  x-intercepts: 1 and 2; $y$-intercept: $- 1$ 
D)  $x$-intercepts: 1 and -2; $y$-intercept: 0

Question 11

Sketch the graph of the polynomial function.
-

Accepted Answer

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

Question 12

Use the graph of a power function and transformations to sketch the graph of the polynomial function.

-$$f ( x ) = - \frac { 1 } { 5 } x ^ { 5 }$$

Accepted Answer

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

Question 13

Find the x- and y-intercepts of f.
-$$f ( x ) = ( x + 3 ) ( x - 4 ) ( x + 4 )$$

Accepted Answer

A)  $x$-intercepts: $- 3 , - 4,4$; y-intercept: $- 48$ 
B)  $x$-intercepts: $- 4,4,3 ;$ y-intercept: 48 
C)  $x$-intercepts: $- 4,4,3$; y-intercept: $- 48$ 
D)  $x$-intercepts: $- 3 , - 4,4$; y-intercept: 48 
A)  $x$-intercepts: $- 3 , - 4,4$; y-intercept: $- 48$ 
B)  $x$-intercepts: $- 4,4,3 ;$ y-intercept: 48 
C)  $x$-intercepts: $- 4,4,3$; y-intercept: $- 48$ 
D)  $x$-intercepts: $- 3 , - 4,4$; y-intercept: 48

Question 14

Use the quadratic function to determine if the function has a maximum or minimum value and then find this maximum or minimum value.
-$$f ( x ) = 3 x ^ { 2 } - 36 x + 113$$

Accepted Answer

A)  maximum at $( 5,6 )$ 
B)  minimum at $( 6,5 )$ 
C)  minimum at $( 6,0 )$ 
D)  maximum at $( 5,0 )$ 
A)  maximum at $( 5,6 )$ 
B)  minimum at $( 6,5 )$ 
C)  minimum at $( 6,0 )$ 
D)  maximum at $( 5,0 )$

Question 15

Solve the problem.
-The profit that the vendor makes per day by selling x pretzels is given by the function $$P ( x ) = - 0.002 x ^ { 2 } + 1.6 x - 150$$ Find the number of pretzels that must be sold to maximize profit.

Accepted Answer

A) 400 pretzels 
B) 170 pretzels 
C) 800 pretzels 
D) 0.8 pretzels 
A) 400 pretzels 
B) 170 pretzels 
C) 800 pretzels 
D) 0.8 pretzels

Question 16

Write the equation of the function in the form f(x)= ax2 + bx + c.
-

Accepted Answer

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

Question 17

Solve the problem.
-A developer wants to enclose a rectangular grassy lot that borders a city street for parking. If the developer has 352 feet of fencing and does not fence the side along the street, what is the largest area that can be enclosed?

Accepted Answer

A)  $23,232 \mathrm { ft } ^ { 2 }$ 
B)  $15,488 \mathrm { ft } ^ { 2 }$ 
C)  $30,976 \mathrm { ft } ^ { 2 }$ 
D)  $7744 \mathrm { ft } ^ { 2 }$ 
A)  $23,232 \mathrm { ft } ^ { 2 }$ 
B)  $15,488 \mathrm { ft } ^ { 2 }$ 
C)  $30,976 \mathrm { ft } ^ { 2 }$ 
D)  $7744 \mathrm { ft } ^ { 2 }$

Question 18

Find the domain of the rational function.
-$$f ( x ) = \frac { x + 7 } { x ^ { 2 } - 1 }$$

Accepted Answer

A)  $\{ x \mid x \neq - 1 , x \neq 1 , x \neq - 7 \}$ 
B)  all real numbers 
C)  $\{ x \mid x \neq 0 , x \neq 1 \}$ 
D)  $\{ x \mid x \neq - 1 , x \neq 1 \}$ 
A)  $\{ x \mid x \neq - 1 , x \neq 1 , x \neq - 7 \}$ 
B)  all real numbers 
C)  $\{ x \mid x \neq 0 , x \neq 1 \}$ 
D)  $\{ x \mid x \neq - 1 , x \neq 1 \}$

Question 19

Solve the variation problem.
-The weight of a liquid varies directly as its volume V. If the weight of the liquid in a cubical container 4 cm on a side is 192 grams, find the weight of the liquid in a cubical container 3 cm on a side.

Accepted Answer

A) 27 grams 
B) 15 grams 
C) 81 grams 
D) 9 grams 
A) 27 grams 
B) 15 grams 
C) 81 grams 
D) 9 grams

Question 20

Graph the function.
-$f(x)=\frac{x^{2}-3 x}{(x-4)^{2}}$

Accepted Answer

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

Graph the function. - $f ( x ) = x ^ { 2 } + \frac { 9 } { x }$ $Graph the function. - f ( x ) = x ^ { 2 } + \frac { 9 } { x }$

Graph the polynomial function. - $f(x)=4 x^{2}-x^{3}$ $Graph the polynomial function. - f(x)=4 x^{2}-x^{3}$

Find the x- and y-intercepts of f. - $f ( x ) = x ^ { 2 } ( x - 2 ) ( x - 1 )$

Give the equation of the slant asymptote, if any, of the function. - $( x ) = \frac { x ^ { 2 } + 5 x - 2 } { x - 7 }$

Graph the function. - $(x)=\frac{x-2}{x^{2}-x-20}$ $Graph the function. - (x)=\frac{x-2}{x^{2}-x-20}$

Use the Factor Theorem to determine whether x - c is a factor of f(x). - $f ( x ) = x ^ { 4 } + 11 x ^ { 3 } + 6 x ^ { 2 } + 64 x - 22 ; x + 11$

Find the axis of symmetry of the quadratic function. - $f ( x ) = - 7 ( x - 2 ) ^ { 2 } - 5$

Find the x- and y-intercepts of f. - $f ( x ) = - x ^ { 2 } ( x + 6 ) \left( x ^ { 2 } + 1 \right)$

Find the range of the quadratic function in interval notation. - $f ( x ) = x ^ { 2 } + 8 x + 6$

First rewrite the quadratic function in standard form by completing the square, then find any x-intercepts and any y-intercepts. - $f ( x ) = x ^ { 2 } + 3 x + 2$

Sketch the graph of the polynomial function. -

Use the graph of a power function and transformations to sketch the graph of the polynomial function. - $f ( x ) = - \frac { 1 } { 5 } x ^ { 5 }$ $Use the graph of a power function and transformations to sketch the graph of the polynomial function. - f ( x ) = - \frac { 1 } { 5 } x ^ { 5 }$

Find the x- and y-intercepts of f. - $f ( x ) = ( x + 3 ) ( x - 4 ) ( x + 4 )$

Use the quadratic function to determine if the function has a maximum or minimum value and then find this maximum or minimum value. - $f ( x ) = 3 x ^ { 2 } - 36 x + 113$

Solve the problem. -The profit that the vendor makes per day by selling x pretzels is given by the function $P ( x ) = - 0.002 x ^ { 2 } + 1.6 x - 150$ Find the number of pretzels that must be sold to maximize profit.

Write the equation of the function in the form f(x)= ax2 + bx + c. -

Solve the problem. -A developer wants to enclose a rectangular grassy lot that borders a city street for parking. If the developer has 352 feet of fencing and does not fence the side along the street, what is the largest area that can be enclosed?

Find the domain of the rational function. - $f ( x ) = \frac { x + 7 } { x ^ { 2 } - 1 }$

Solve the variation problem. -The weight of a liquid varies directly as its volume V. If the weight of the liquid in a cubical container 4 cm on a side is 192 grams, find the weight of the liquid in a cubical container 3 cm on a side.

Graph the function. - $f(x)=\frac{x^{2}-3 x}{(x-4)^{2}}$ $Graph the function. - f(x)=\frac{x^{2}-3 x}{(x-4)^{2}}$

Equations, Inequalities, and Applications

The Rectangular Coordinate System, Lines, and Circles

Functions

Exponential and Logarithmic Functions and Equations

Conic Sections

Systems of Equations and Inequalities

Matrices

Sequences and Series; Counting and Probability

Math Exercises: Sets, Intervals, Absolute Value, and Properties

Filters

Exam 4: Polynomial and Rational Functions

Graph the function. - f(x)=x2+9xf ( x ) = x ^ { 2 } + \frac { 9 } { x }f(x)=x2+x9​

Graph the polynomial function. - f(x)=4x2−x3f(x)=4 x^{2}-x^{3}f(x)=4x2−x3

Find the x- and y-intercepts of f. - f(x)=x2(x−2)(x−1)f ( x ) = x ^ { 2 } ( x - 2 ) ( x - 1 )f(x)=x2(x−2)(x−1)

Give the equation of the slant asymptote, if any, of the function. - (x)=x2+5x−2x−7( x ) = \frac { x ^ { 2 } + 5 x - 2 } { x - 7 }(x)=x−7x2+5x−2​

Graph the function. - (x)=x−2x2−x−20(x)=\frac{x-2}{x^{2}-x-20}(x)=x2−x−20x−2​

Use the Factor Theorem to determine whether x - c is a factor of f(x). - f(x)=x4+11x3+6x2+64x−22;x+11f ( x ) = x ^ { 4 } + 11 x ^ { 3 } + 6 x ^ { 2 } + 64 x - 22 ; x + 11f(x)=x4+11x3+6x2+64x−22;x+11

Find the axis of symmetry of the quadratic function. - f(x)=−7(x−2)2−5f ( x ) = - 7 ( x - 2 ) ^ { 2 } - 5f(x)=−7(x−2)2−5

Find the x- and y-intercepts of f. - f(x)=−x2(x+6)(x2+1)f ( x ) = - x ^ { 2 } ( x + 6 ) \left( x ^ { 2 } + 1 \right)f(x)=−x2(x+6)(x2+1)

Find the range of the quadratic function in interval notation. - f(x)=x2+8x+6f ( x ) = x ^ { 2 } + 8 x + 6f(x)=x2+8x+6

First rewrite the quadratic function in standard form by completing the square, then find any x-intercepts and any y-intercepts. - f(x)=x2+3x+2f ( x ) = x ^ { 2 } + 3 x + 2f(x)=x2+3x+2

Sketch the graph of the polynomial function. -

Use the graph of a power function and transformations to sketch the graph of the polynomial function. - f(x)=−15x5f ( x ) = - \frac { 1 } { 5 } x ^ { 5 }f(x)=−51​x5

Find the x- and y-intercepts of f. - f(x)=(x+3)(x−4)(x+4)f ( x ) = ( x + 3 ) ( x - 4 ) ( x + 4 )f(x)=(x+3)(x−4)(x+4)

Use the quadratic function to determine if the function has a maximum or minimum value and then find this maximum or minimum value. - f(x)=3x2−36x+113f ( x ) = 3 x ^ { 2 } - 36 x + 113f(x)=3x2−36x+113

Solve the problem. -The profit that the vendor makes per day by selling x pretzels is given by the function P(x)=−0.002x2+1.6x−150P ( x ) = - 0.002 x ^ { 2 } + 1.6 x - 150P(x)=−0.002x2+1.6x−150 Find the number of pretzels that must be sold to maximize profit.

Write the equation of the function in the form f(x)= ax2 + bx + c. -

Solve the problem. -A developer wants to enclose a rectangular grassy lot that borders a city street for parking. If the developer has 352 feet of fencing and does not fence the side along the street, what is the largest area that can be enclosed?

Find the domain of the rational function. - f(x)=x+7x2−1f ( x ) = \frac { x + 7 } { x ^ { 2 } - 1 }f(x)=x2−1x+7​

Solve the variation problem. -The weight of a liquid varies directly as its volume V. If the weight of the liquid in a cubical container 4 cm on a side is 192 grams, find the weight of the liquid in a cubical container 3 cm on a side.

Graph the function. - f(x)=x2−3x(x−4)2f(x)=\frac{x^{2}-3 x}{(x-4)^{2}}f(x)=(x−4)2x2−3x​

Equations, Inequalities, and Applications

The Rectangular Coordinate System, Lines, and Circles

Functions

Exponential and Logarithmic Functions and Equations

Conic Sections

Systems of Equations and Inequalities

Matrices

Sequences and Series; Counting and Probability

Math Exercises: Sets, Intervals, Absolute Value, and Properties

Filters

Graph the function. - $f ( x ) = x ^ { 2 } + \frac { 9 } { x }$ $Graph the function. - f ( x ) = x ^ { 2 } + \frac { 9 } { x }$

Graph the polynomial function. - $f(x)=4 x^{2}-x^{3}$ $Graph the polynomial function. - f(x)=4 x^{2}-x^{3}$

Find the x- and y-intercepts of f. - $f ( x ) = x ^ { 2 } ( x - 2 ) ( x - 1 )$

Give the equation of the slant asymptote, if any, of the function. - $( x ) = \frac { x ^ { 2 } + 5 x - 2 } { x - 7 }$

Graph the function. - $(x)=\frac{x-2}{x^{2}-x-20}$ $Graph the function. - (x)=\frac{x-2}{x^{2}-x-20}$

Use the Factor Theorem to determine whether x - c is a factor of f(x). - $f ( x ) = x ^ { 4 } + 11 x ^ { 3 } + 6 x ^ { 2 } + 64 x - 22 ; x + 11$

Find the axis of symmetry of the quadratic function. - $f ( x ) = - 7 ( x - 2 ) ^ { 2 } - 5$

Find the x- and y-intercepts of f. - $f ( x ) = - x ^ { 2 } ( x + 6 ) \left( x ^ { 2 } + 1 \right)$

Find the range of the quadratic function in interval notation. - $f ( x ) = x ^ { 2 } + 8 x + 6$

First rewrite the quadratic function in standard form by completing the square, then find any x-intercepts and any y-intercepts. - $f ( x ) = x ^ { 2 } + 3 x + 2$

Use the graph of a power function and transformations to sketch the graph of the polynomial function. - $f ( x ) = - \frac { 1 } { 5 } x ^ { 5 }$ $Use the graph of a power function and transformations to sketch the graph of the polynomial function. - f ( x ) = - \frac { 1 } { 5 } x ^ { 5 }$

Find the x- and y-intercepts of f. - $f ( x ) = ( x + 3 ) ( x - 4 ) ( x + 4 )$

Use the quadratic function to determine if the function has a maximum or minimum value and then find this maximum or minimum value. - $f ( x ) = 3 x ^ { 2 } - 36 x + 113$

Solve the problem. -The profit that the vendor makes per day by selling x pretzels is given by the function $P ( x ) = - 0.002 x ^ { 2 } + 1.6 x - 150$ Find the number of pretzels that must be sold to maximize profit.

Find the domain of the rational function. - $f ( x ) = \frac { x + 7 } { x ^ { 2 } - 1 }$

Graph the function. - $f(x)=\frac{x^{2}-3 x}{(x-4)^{2}}$ $Graph the function. - f(x)=\frac{x^{2}-3 x}{(x-4)^{2}}$