Question 1

Find the coordinates of the vertex for the parabola defined by the given quadratic function.
-$$f ( x ) = x ^ { 2 } - 9$$

Accepted Answer

A)  $( 0 , - 9 )$ 
B)  $( 1,0 )$ 
C)  $( 0,9 )$ 
D)  $( 9,0 )$ 
A)  $( 0 , - 9 )$ 
B)  $( 1,0 )$ 
C)  $( 0,9 )$ 
D)  $( 9,0 )$

Question 2

Find the y-intercept of the polynomial function.
-$$f ( x ) = - x ^ { 3 } ( x + 3 ) ^ { 2 } ( x - 6 )$$

Accepted Answer

A)  origin symmetry 
B)  $y$-axis symmetry 
C)  neither 
A)  origin symmetry 
B)  $y$-axis symmetry 
C)  neither

Question 3

Find the vertical asymptotes, if any, of the graph of the rational function.
-$$f ( x ) = \frac { x } { x ^ { 2 } + 7 }$$

Accepted Answer

A)  $x = - 7$ 
B)  $x = - 7 , x = 7$ 
C)  $x = 7$ 
D)  no vertical asymptote 
A)  $x = - 7$ 
B)  $x = - 7 , x = 7$ 
C)  $x = 7$ 
D)  no vertical asymptote

Question 4

Choose the one alternative that best completes the statement or answers the question.
Use the vertex and intercepts to sketch the graph of the quadratic function.
-$f(x)=-x^{2}+2 x+3$

Accepted Answer

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

Question 5

Find the y-intercept of the polynomial function.
-$$f ( x ) = - x ^ { 2 } - 2 x + 3$$

Accepted Answer

A)  3 
B)  $- 3$ 
C)  0 
D)  $- 1$ 
A)  3 
B)  $- 3$ 
C)  0 
D)  $- 1$

Question 6

The graph of a quadratic function is given. Determine the function's equation.
-

Accepted Answer

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

Question 7

Find the domain and range of the quadratic function whose graph is described.
-The maximum is $- 3$ at $x = - 1$

Accepted Answer

A)  Domain: $( - \infty , \infty )$
Range: $( - \infty , - 3 ]$ 
B)  Domain: $( - \infty , - 1 ]$
Range: $( - \infty , - 3 ]$ 
C)  Domain: $( - \infty , \infty )$
Range: $[ - 3 , \infty )$ 
D)  Domain: $( - \infty , \infty )$
Range: $( - \infty , - 1 ]$ 
A)  Domain: $( - \infty , \infty )$
Range: $( - \infty , - 3 ]$ 
B)  Domain: $( - \infty , - 1 ]$
Range: $( - \infty , - 3 ]$ 
C)  Domain: $( - \infty , \infty )$
Range: $[ - 3 , \infty )$ 
D)  Domain: $( - \infty , \infty )$
Range: $( - \infty , - 1 ]$

Question 8

Find the horizontal asymptote, if any, of the graph of the rational function.
-$$h ( x ) = \frac { 8 x ^ { 3 } } { 2 x ^ { 2 } + 1 }$$

Accepted Answer

A)  $y = 4$ 
B)  $y = 0$ 
C)  $\mathrm { y } = \frac { 1 } { 4 }$ 
D)  no horizontal asymptote 
A)  $y = 4$ 
B)  $y = 0$ 
C)  $\mathrm { y } = \frac { 1 } { 4 }$ 
D)  no horizontal asymptote

Question 9

Determine the maximum possible number of turning points for the graph of the function.
-The profits (in millions) for a company for 8 years were as follows:

Which of the following polynomials is the best model for this data?

Accepted Answer

A)  $P ( x ) = 0.05 x ^ { 2 } - 0.8 x + 6$ 
B)  $P ( x ) = - 0.08 x ^ { 3 } + 7 x ^ { 2 } + 1.3 x - 0.18$ 
C)  $P ( x ) = 0.03 x ^ { 3 } - 0.3 x ^ { 2 } + 1.3 x + 0.17$ 
D)  $P ( x ) = - 0.03 x ^ { 4 } - 0.3 x ^ { 2 } + 1.3 x + 0.17$ 
A)  $P ( x ) = 0.05 x ^ { 2 } - 0.8 x + 6$ 
B)  $P ( x ) = - 0.08 x ^ { 3 } + 7 x ^ { 2 } + 1.3 x - 0.18$ 
C)  $P ( x ) = 0.03 x ^ { 3 } - 0.3 x ^ { 2 } + 1.3 x + 0.17$ 
D)  $P ( x ) = - 0.03 x ^ { 4 } - 0.3 x ^ { 2 } + 1.3 x + 0.17$

Question 10

Determine whether the function is a polynomial function.
-$$g ( x ) = 9 x ^ { 7 } + 6$$

Accepted Answer

A)  7 
B)  8 
C)  0 
D)  9 
A)  7 
B)  8 
C)  0 
D)  9

Question 11

Use synthetic division and the Remainder Theorem to find the indicated function value.
-$$f ( x ) = x ^ { 5 } + 8 x ^ { 4 } - 6 x ^ { 3 } + 6 ; f ( - 4 )$$

Accepted Answer

A)  1414 
B)  $- 1414$ 
C)  94 
D)  2438 
A)  1414 
B)  $- 1414$ 
C)  94 
D)  2438

Question 12

Graph the rational function.
-$$f ( x ) = - \frac { 4 } { x ^ { 2 } - 9 }$$

Accepted Answer

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

Question 13

Find the y-intercept of the polynomial function.
-$$f ( x ) = ( x + 1 ) ( x - 2 ) ( x - 1 ) ^ { 2 }$$

Accepted Answer

A)  $- 2$ 
B)  2 
C)  0 
D)  $- 1$ 
A)  $- 2$ 
B)  2 
C)  0 
D)  $- 1$

Question 14

Find the coordinates of the vertex for the parabola defined by the given quadratic function.
-$$f ( x ) = ( x - 1 ) ^ { 2 } - 1$$

Accepted Answer

A)  $( 1 , - 1 )$ 
B)  $( 1,1 )$ 
C)  $( 0 , - 1 )$ 
D)  $( - 1,0 )$ 
A)  $( 1 , - 1 )$ 
B)  $( 1,1 )$ 
C)  $( 0 , - 1 )$ 
D)  $( - 1,0 )$

Question 15

Solve Combined Variation Problems
-$\mathrm { p }$ varies directly as $\mathrm { q }$ and inversely as the square of $r$.

Accepted Answer

A)  $\mathrm { p } = \frac { \mathrm { kq } } { \mathrm { r } ^ { 2 } }$ 
B)  $\mathrm { p } = \frac { \mathrm { kr } } { }$ 
C)  $\mathrm { pqr } ^ { 2 } = \mathrm { k }$ 
D)  $\mathrm { p } + \mathrm { q } - \mathrm { r } ^ { 2 } = \mathrm { k }$ 
A)  $\mathrm { p } = \frac { \mathrm { kq } } { \mathrm { r } ^ { 2 } }$ 
B)  $\mathrm { p } = \frac { \mathrm { kr } } { }$ 
C)  $\mathrm { pqr } ^ { 2 } = \mathrm { k }$ 
D)  $\mathrm { p } + \mathrm { q } - \mathrm { r } ^ { 2 } = \mathrm { k }$

Question 16

Graph the rational function.
-$$f ( x ) = \frac { 5 x ^ { 2 } } { x ^ { 2 } + 25 }$$

Accepted Answer

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

Question 17

Divide using synthetic division.
-$$\left( x ^ { 2 } + 16 x + 63 \right) \div ( x + 7 )$$

Accepted Answer

A)  $x + 9$ 
B)  $x - 56$ 
C)  $x ^ { 2 } + 9$ 
D)  $x ^ { 3 } - 56$ 
A)  $x + 9$ 
B)  $x - 56$ 
C)  $x ^ { 2 } + 9$ 
D)  $x ^ { 3 } - 56$

Question 18

Use the Rational Zero Theorem to list all possible rational zeros for the given function.
-$$f ( x ) = 3 x ^ { 4 } + 5 x ^ { 3 } - 6 x ^ { 2 } + 6 x - 12$$

Accepted Answer

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

Question 19

Find the y-intercept of the polynomial function.
-

Accepted Answer

A)  $y$-axis symmetry 
B)  origin symmetry 
C)  neither 
A)  $y$-axis symmetry 
B)  origin symmetry 
C)  neither

Question 20

Graph the rational function.
-$$f ( x ) = \frac { x ^ { 2 } - 6 x + 5 } { x ^ { 2 } + 4 }$$

Accepted Answer

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

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = x ^ { 2 } - 9$

Find the y-intercept of the polynomial function. - $f ( x ) = - x ^ { 3 } ( x + 3 ) ^ { 2 } ( x - 6 )$

Find the vertical asymptotes, if any, of the graph of the rational function. - $f ( x ) = \frac { x } { x ^ { 2 } + 7 }$

Find the y-intercept of the polynomial function. - $f ( x ) = - x ^ { 2 } - 2 x + 3$

The graph of a quadratic function is given. Determine the function's equation. -

Find the domain and range of the quadratic function whose graph is described. -The maximum is $- 3$ at $x = - 1$

Find the horizontal asymptote, if any, of the graph of the rational function. - $h ( x ) = \frac { 8 x ^ { 3 } } { 2 x ^ { 2 } + 1 }$

Determine the maximum possible number of turning points for the graph of the function. -The profits (in millions) for a company for 8 years were as follows: Which of the following polynomials is the best model for this data?

Determine whether the function is a polynomial function. - $g ( x ) = 9 x ^ { 7 } + 6$

Use synthetic division and the Remainder Theorem to find the indicated function value. - $f ( x ) = x ^ { 5 } + 8 x ^ { 4 } - 6 x ^ { 3 } + 6 ; f ( - 4 )$

Graph the rational function. - $f ( x ) = - \frac { 4 } { x ^ { 2 } - 9 }$ $Graph the rational function. - f ( x ) = - \frac { 4 } { x ^ { 2 } - 9 }$

Find the y-intercept of the polynomial function. - $f ( x ) = ( x + 1 ) ( x - 2 ) ( x - 1 ) ^ { 2 }$

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = ( x - 1 ) ^ { 2 } - 1$

Solve Combined Variation Problems - $\mathrm { p }$ varies directly as $\mathrm { q }$ and inversely as the square of $r$ .

Graph the rational function. - $f ( x ) = \frac { 5 x ^ { 2 } } { x ^ { 2 } + 25 }$ $Graph the rational function. - f ( x ) = \frac { 5 x ^ { 2 } } { x ^ { 2 } + 25 }$

Divide using synthetic division. - $\left( x ^ { 2 } + 16 x + 63 \right) \div ( x + 7 )$

Use the Rational Zero Theorem to list all possible rational zeros for the given function. - $f ( x ) = 3 x ^ { 4 } + 5 x ^ { 3 } - 6 x ^ { 2 } + 6 x - 12$

Find the y-intercept of the polynomial function. -

Graph the rational function. - $f ( x ) = \frac { x ^ { 2 } - 6 x + 5 } { x ^ { 2 } + 4 }$ $Graph the rational function. - f ( x ) = \frac { x ^ { 2 } - 6 x + 5 } { x ^ { 2 } + 4 }$

Equations and Inequalities

Functions and Graphs

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Systems of Equations and Inequalities

Matrices and Determinants

Conic Sections and Analytic Geometry

Sequences, Induction, and Probability

Prerequisites: Fundamental Concepts of Algebra

Filters

Exam 3: Polynomial and Rational Functions

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - f(x)=x2−9f ( x ) = x ^ { 2 } - 9f(x)=x2−9

Find the y-intercept of the polynomial function. - f(x)=−x3(x+3)2(x−6)f ( x ) = - x ^ { 3 } ( x + 3 ) ^ { 2 } ( x - 6 )f(x)=−x3(x+3)2(x−6)

Find the vertical asymptotes, if any, of the graph of the rational function. - f(x)=xx2+7f ( x ) = \frac { x } { x ^ { 2 } + 7 }f(x)=x2+7x​

Choose the one alternative that best completes the statement or answers the question. Use the vertex and intercepts to sketch the graph of the quadratic function. - f(x)=−x2+2x+3f(x)=-x^{2}+2 x+3f(x)=−x2+2x+3

Find the y-intercept of the polynomial function. - f(x)=−x2−2x+3f ( x ) = - x ^ { 2 } - 2 x + 3f(x)=−x2−2x+3

The graph of a quadratic function is given. Determine the function's equation. -

Find the domain and range of the quadratic function whose graph is described. -The maximum is −3- 3−3 at x=−1x = - 1x=−1

Find the horizontal asymptote, if any, of the graph of the rational function. - h(x)=8x32x2+1h ( x ) = \frac { 8 x ^ { 3 } } { 2 x ^ { 2 } + 1 }h(x)=2x2+18x3​

Determine the maximum possible number of turning points for the graph of the function. -The profits (in millions) for a company for 8 years were as follows: Which of the following polynomials is the best model for this data?

Determine whether the function is a polynomial function. - g(x)=9x7+6g ( x ) = 9 x ^ { 7 } + 6g(x)=9x7+6

Use synthetic division and the Remainder Theorem to find the indicated function value. - f(x)=x5+8x4−6x3+6;f(−4)f ( x ) = x ^ { 5 } + 8 x ^ { 4 } - 6 x ^ { 3 } + 6 ; f ( - 4 )f(x)=x5+8x4−6x3+6;f(−4)

Graph the rational function. - f(x)=−4x2−9f ( x ) = - \frac { 4 } { x ^ { 2 } - 9 }f(x)=−x2−94​

Find the y-intercept of the polynomial function. - f(x)=(x+1)(x−2)(x−1)2f ( x ) = ( x + 1 ) ( x - 2 ) ( x - 1 ) ^ { 2 }f(x)=(x+1)(x−2)(x−1)2

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - f(x)=(x−1)2−1f ( x ) = ( x - 1 ) ^ { 2 } - 1f(x)=(x−1)2−1

Solve Combined Variation Problems - p\mathrm { p }p varies directly as q\mathrm { q }q and inversely as the square of rrr .

Graph the rational function. - f(x)=5x2x2+25f ( x ) = \frac { 5 x ^ { 2 } } { x ^ { 2 } + 25 }f(x)=x2+255x2​

Divide using synthetic division. - (x2+16x+63)÷(x+7)\left( x ^ { 2 } + 16 x + 63 \right) \div ( x + 7 )(x2+16x+63)÷(x+7)

Use the Rational Zero Theorem to list all possible rational zeros for the given function. - f(x)=3x4+5x3−6x2+6x−12f ( x ) = 3 x ^ { 4 } + 5 x ^ { 3 } - 6 x ^ { 2 } + 6 x - 12f(x)=3x4+5x3−6x2+6x−12

Find the y-intercept of the polynomial function. -

Graph the rational function. - f(x)=x2−6x+5x2+4f ( x ) = \frac { x ^ { 2 } - 6 x + 5 } { x ^ { 2 } + 4 }f(x)=x2+4x2−6x+5​

Equations and Inequalities

Functions and Graphs

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Systems of Equations and Inequalities

Matrices and Determinants

Conic Sections and Analytic Geometry

Sequences, Induction, and Probability

Prerequisites: Fundamental Concepts of Algebra

Filters

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = x ^ { 2 } - 9$

Find the y-intercept of the polynomial function. - $f ( x ) = - x ^ { 3 } ( x + 3 ) ^ { 2 } ( x - 6 )$

Find the vertical asymptotes, if any, of the graph of the rational function. - $f ( x ) = \frac { x } { x ^ { 2 } + 7 }$

Find the y-intercept of the polynomial function. - $f ( x ) = - x ^ { 2 } - 2 x + 3$

Find the domain and range of the quadratic function whose graph is described. -The maximum is $- 3$ at $x = - 1$

Find the horizontal asymptote, if any, of the graph of the rational function. - $h ( x ) = \frac { 8 x ^ { 3 } } { 2 x ^ { 2 } + 1 }$

Determine whether the function is a polynomial function. - $g ( x ) = 9 x ^ { 7 } + 6$

Use synthetic division and the Remainder Theorem to find the indicated function value. - $f ( x ) = x ^ { 5 } + 8 x ^ { 4 } - 6 x ^ { 3 } + 6 ; f ( - 4 )$

Graph the rational function. - $f ( x ) = - \frac { 4 } { x ^ { 2 } - 9 }$ $Graph the rational function. - f ( x ) = - \frac { 4 } { x ^ { 2 } - 9 }$

Find the y-intercept of the polynomial function. - $f ( x ) = ( x + 1 ) ( x - 2 ) ( x - 1 ) ^ { 2 }$

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = ( x - 1 ) ^ { 2 } - 1$

Solve Combined Variation Problems - $\mathrm { p }$ varies directly as $\mathrm { q }$ and inversely as the square of $r$ .

Graph the rational function. - $f ( x ) = \frac { 5 x ^ { 2 } } { x ^ { 2 } + 25 }$ $Graph the rational function. - f ( x ) = \frac { 5 x ^ { 2 } } { x ^ { 2 } + 25 }$

Divide using synthetic division. - $\left( x ^ { 2 } + 16 x + 63 \right) \div ( x + 7 )$

Use the Rational Zero Theorem to list all possible rational zeros for the given function. - $f ( x ) = 3 x ^ { 4 } + 5 x ^ { 3 } - 6 x ^ { 2 } + 6 x - 12$

Graph the rational function. - $f ( x ) = \frac { x ^ { 2 } - 6 x + 5 } { x ^ { 2 } + 4 }$ $Graph the rational function. - f ( x ) = \frac { x ^ { 2 } - 6 x + 5 } { x ^ { 2 } + 4 }$