Question 1

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

Accepted Answer

A)  $\pm \frac { 1 } { 5 } , \pm \frac { 3 } { 5 } , \pm 1 , \pm 3$ 
B)  $\pm \frac { 1 } { 3 } , \pm \frac { 5 } { 3 } , \pm 1 , \pm 5$ 
C)  $\pm \frac { 1 } { 5 } , \pm \frac { 3 } { 5 } , \pm 1 , \pm 3 , \pm 5$ 
D)  $\pm \frac { 1 } { 5 } , \pm \frac { 1 } { 3 } , \pm 1 , \pm 3 , \pm 5$ 
A)  $\pm \frac { 1 } { 5 } , \pm \frac { 3 } { 5 } , \pm 1 , \pm 3$ 
B)  $\pm \frac { 1 } { 3 } , \pm \frac { 5 } { 3 } , \pm 1 , \pm 5$ 
C)  $\pm \frac { 1 } { 5 } , \pm \frac { 3 } { 5 } , \pm 1 , \pm 3 , \pm 5$ 
D)  $\pm \frac { 1 } { 5 } , \pm \frac { 1 } { 3 } , \pm 1 , \pm 3 , \pm 5$

Question 2

Divide using long division.
-$$\frac { 4 x ^ { 3 } - 43 x + 21 } { x - 3 }$$

Accepted Answer

A)  $4 x ^ { 2 } + 12 x - 7$ 
B)  $4 x ^ { 2 } - 31 x + \frac { - 72 } { x - 3 }$ 
C)  $4 x ^ { 2 } + 31 x + \frac { - 72 } { x - 3 }$ 
D)  $4 x ^ { 2 } - 12 x - 7$ 
A)  $4 x ^ { 2 } + 12 x - 7$ 
B)  $4 x ^ { 2 } - 31 x + \frac { - 72 } { x - 3 }$ 
C)  $4 x ^ { 2 } + 31 x + \frac { - 72 } { x - 3 }$ 
D)  $4 x ^ { 2 } - 12 x - 7$

Question 3

Find an nth degree polynomial function with real coefficients satisfying the given conditions.
-$\mathrm { n } = 3 ; - 4$ and $\mathrm { i }$ are zeros; $\mathrm { f } ( - 3 ) = 60$

Accepted Answer

A)  $f ( x ) = 6 x ^ { 3 } + 24 x ^ { 2 } + 6 x + 24$ 
B)  $f ( x ) = 6 x ^ { 3 } + 24 x ^ { 2 } - 6 x - 24$ 
C)  $f ( x ) = - 6 x ^ { 3 } - 24 x ^ { 2 } - 6 x - 24$ 
D)  $f ( x ) = - 6 x ^ { 3 } - 24 x ^ { 2 } + 6 x + 24$ 
A)  $f ( x ) = 6 x ^ { 3 } + 24 x ^ { 2 } + 6 x + 24$ 
B)  $f ( x ) = 6 x ^ { 3 } + 24 x ^ { 2 } - 6 x - 24$ 
C)  $f ( x ) = - 6 x ^ { 3 } - 24 x ^ { 2 } - 6 x - 24$ 
D)  $f ( x ) = - 6 x ^ { 3 } - 24 x ^ { 2 } + 6 x + 24$

Question 4

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

Accepted Answer

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

Question 5

Divide using long division.
-$\frac { 8 m ^ { 3 } + 44 m ^ { 2 } - 15 m + 54 } { m + 6 }$

Accepted Answer

A)  $8 m ^ { 2 } - 4 m + 9$ 
B)  $8 m ^ { 2 } + 4 m + 9$ 
C)  $m ^ { 2 } + 5 m + 6$ 
D)  $m ^ { 2 } + 4 m + 8$ 
A)  $8 m ^ { 2 } - 4 m + 9$ 
B)  $8 m ^ { 2 } + 4 m + 9$ 
C)  $m ^ { 2 } + 5 m + 6$ 
D)  $m ^ { 2 } + 4 m + 8$

Question 6

Solve the polynomial equation. In order to obtain the first root, use synthetic division to test the possible rational
roots.
-$$x ^ { 3 } - 5 x ^ { 2 } + 6 x - 2 = 0$$

Accepted Answer

A)  $\{ 1,2 + \sqrt { 2 } , 2 - \sqrt { 2 } \}$ 
B)  $\{ 1 , - 1,2 \}$ 
C)  $\{ - 1,4 + \sqrt { 2 } , 4 - \sqrt { 2 } \}$ 
D)  $\{ 1,4 + \sqrt { 2 } , 4 - \sqrt { 2 } \}$ 
A)  $\{ 1,2 + \sqrt { 2 } , 2 - \sqrt { 2 } \}$ 
B)  $\{ 1 , - 1,2 \}$ 
C)  $\{ - 1,4 + \sqrt { 2 } , 4 - \sqrt { 2 } \}$ 
D)  $\{ 1,4 + \sqrt { 2 } , 4 - \sqrt { 2 } \}$

Question 7

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

Accepted Answer

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

Question 8

Find the x-intercepts (if any) for the graph of the quadratic function.
-$$f ( x ) = 2 x ^ { 2 } - 5 x - 3$$

Accepted Answer

A)  $( 3,0 )$ and $( - 0.5,0 )$ 
B)  $( 3,0 )$ and $( 0.5,0 )$ 
C)  $( - 1,0 )$ and $( 1.5,0 )$ 
D)  $( - 1,0 )$ and $( - 1.5,0 )$ 
A)  $( 3,0 )$ and $( - 0.5,0 )$ 
B)  $( 3,0 )$ and $( 0.5,0 )$ 
C)  $( - 1,0 )$ and $( 1.5,0 )$ 
D)  $( - 1,0 )$ and $( - 1.5,0 )$

Question 9

Solve the polynomial equation. In order to obtain the first root, use synthetic division to test the possible rational
roots.
-$$3 \mathrm { x } ^ { 3 } - \mathrm { x } ^ { 2 } - 15 \mathrm { x } + 5 = 0$$

Accepted Answer

A)  $\left\{ \frac { 1 } { 3 } , \sqrt { 5 } , - \sqrt { 5 } \right\}$ 
B)  $\left\{ - \frac { 1 } { 3 } , \sqrt { 5 } , - \sqrt { 5 } \right\}$ 
C)  $\{ 3 , \sqrt { 5 } , - \sqrt { 5 } \}$ 
D)  $\{ - 3 , \sqrt { 5 } , - \sqrt { 5 } \}$ 
A)  $\left\{ \frac { 1 } { 3 } , \sqrt { 5 } , - \sqrt { 5 } \right\}$ 
B)  $\left\{ - \frac { 1 } { 3 } , \sqrt { 5 } , - \sqrt { 5 } \right\}$ 
C)  $\{ 3 , \sqrt { 5 } , - \sqrt { 5 } \}$ 
D)  $\{ - 3 , \sqrt { 5 } , - \sqrt { 5 } \}$

Question 10

Determine the constant of variation for the stated condition.
-The amount of gas that a helicopter uses is directly proportional to the number of hours spent flying. The helicopter flies for 2 hours and uses 30 gallons of fuel. Find the number of gallons of fuel that the helicopter uses to fly for 3 hours.

Accepted Answer

A)  45 gallons 
B)  6 gallons 
C)  48 gallons 
D)  60 gallons 
A)  45 gallons 
B)  6 gallons 
C)  48 gallons 
D)  60 gallons

Question 11

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

Accepted Answer

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

Question 12

Determine the constant of variation for the stated condition.
-The volume $\mathrm { V }$ of a given mass of gas varies directly as the temperature $\mathrm { T }$ and inversely as the pressure $\mathrm { P }$. A measuring device is calibrated to give $\mathrm { V } = 216 \mathrm { in } ^ { 3 }$ when $\mathrm { T } = 450 ^ { \circ }$ and $\mathrm { P } = 25 \mathrm { lb } / \mathrm { in } ^ { 2 }$. What is the volume on this device when the temperature is $500 ^ { \circ }$ and the pressure is $20 \mathrm { lb } / \mathrm { in } ^ { 2 } ?$

Accepted Answer

A)  $V = 300$ in $^ { 3 }$ 
B)  $\mathrm { V } = 25 \mathrm { in } ^ { 3 }$ 
C)  $V = 320$ in $^ { 3 }$ 
D)  $V = 280$ in $^ { 3 }$ 
A)  $V = 300$ in $^ { 3 }$ 
B)  $\mathrm { V } = 25 \mathrm { in } ^ { 3 }$ 
C)  $V = 320$ in $^ { 3 }$ 
D)  $V = 280$ in $^ { 3 }$

Question 13

Find the x-intercepts (if any) for the graph of the quadratic function.
-$f ( x ) = x ^ { 2 } + 12 x + 15$ Give your answers in exact form.

Accepted Answer

A)  $( - 6 \pm \sqrt { 21 } , 0 )$ 
B)  $( 6 + \sqrt { 21 } , 0 )$ 
C)  $( 6 \pm \sqrt { 15 } , 0 )$ 
D)  $( - 12 \pm \sqrt { 15 } , 0 )$ 
A)  $( - 6 \pm \sqrt { 21 } , 0 )$ 
B)  $( 6 + \sqrt { 21 } , 0 )$ 
C)  $( 6 \pm \sqrt { 15 } , 0 )$ 
D)  $( - 12 \pm \sqrt { 15 } , 0 )$

Question 14

Use the Intermediate Value Theorem to determine whether the polynomial function has a real zero between the
given integers.
-$f ( x ) = - 3 x ^ { 4 } - 4 x ^ { 3 } + 9 x + 3 ;$ between 1 and 2

Accepted Answer

A)  $f ( 1 ) = 5$ and $f ( 2 ) = - 59$; yes 
B)  $f ( 1 ) = 5$ and $f ( 2 ) = 59$; no 
C)  $f ( 1 ) = - 5$ and $f ( 2 ) = - 59$; no 
D)  $f ( 1 ) = - 5$ and $f ( 2 ) = 59$; yes 
A)  $f ( 1 ) = 5$ and $f ( 2 ) = - 59$; yes 
B)  $f ( 1 ) = 5$ and $f ( 2 ) = 59$; no 
C)  $f ( 1 ) = - 5$ and $f ( 2 ) = - 59$; no 
D)  $f ( 1 ) = - 5$ and $f ( 2 ) = 59$; yes

Question 15

Find the coordinates of the vertex for the parabola defined by the given quadratic function.
-$$f ( x ) = - 3 x ^ { 2 } + 6 x + 1$$

Accepted Answer

A)  $( 1,4 )$ 
B)  $( - 1 , - 8 )$ 
C)  $( 2 , - 5 )$ 
D)  $( - 2 , - 23 )$ 
A)  $( 1,4 )$ 
B)  $( - 1 , - 8 )$ 
C)  $( 2 , - 5 )$ 
D)  $( - 2 , - 23 )$

Question 16

Solve the problem.
-A rectangular playground is to be fenced off and divided in two by another fence parallel to one side of the playground. 624 feet of fencing is used. Find the maximum area of the playground.

Accepted Answer

A)  $16,224 \mathrm { ft } ^ { 2 }$ 
B)  $24,336 \mathrm { ft } ^ { 2 }$ 
C)  $12,168 \mathrm { ft } ^ { 2 }$ 
D)  $18,252 \mathrm { ft } ^ { 2 }$ 
A)  $16,224 \mathrm { ft } ^ { 2 }$ 
B)  $24,336 \mathrm { ft } ^ { 2 }$ 
C)  $12,168 \mathrm { ft } ^ { 2 }$ 
D)  $18,252 \mathrm { ft } ^ { 2 }$

Question 17

Determine whether the function is a polynomial function.
-$$7 x ^ { 4 } - 3 x ^ { 3 } - 4 x - 2 y ^ { 5 } + 5$$

Accepted Answer

A)  5 
B)  4 
C)  13 
D)  7 
A)  5 
B)  4 
C)  13 
D)  7

Question 18

x Find the range of the quadratic function.
-$$f ( x ) = 7 - ( x + 2 ) ^ { 2 }$$

Accepted Answer

A)  $( - \infty , 7 ]$ 
B)  $[ 7 , \infty )$ 
C)  $( - \infty , 2 ]$ 
D)  $[ - 2 , \infty )$ 
A)  $( - \infty , 7 ]$ 
B)  $[ 7 , \infty )$ 
C)  $( - \infty , 2 ]$ 
D)  $[ - 2 , \infty )$

Question 19

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

Accepted Answer

A)  $j ( x ) = x ^ { 2 } + 3$ 
B)  $g ( x ) = x ^ { 2 } + 6 x + 9$ 
C)  $h ( x ) = x ^ { 2 } - 3$ 
D)  $f ( x ) = x ^ { 2 } - 6 x + 9$ 
A)  $j ( x ) = x ^ { 2 } + 3$ 
B)  $g ( x ) = x ^ { 2 } + 6 x + 9$ 
C)  $h ( x ) = x ^ { 2 } - 3$ 
D)  $f ( x ) = x ^ { 2 } - 6 x + 9$

Question 20

Find the domain and range of the quadratic function whose graph is described.
-The minimum is $- 6$ at $x = - 1$.

Accepted Answer

A)  Domain: $( - \infty , \infty )$
Range: $[ - 6 , \infty )$ 
B)  Domain: $[ - 1 , \infty )$
Range: $[ - 6 , \infty )$ 
C)  Domain: $( - \infty , \infty )$
Range: $[- \infty , -\ 6] $ 
D)  Domain: $( - \infty , \infty )$ 
Range: $[- \ 1 , \infty ] $ 
A)  Domain: $( - \infty , \infty )$
Range: $[ - 6 , \infty )$ 
B)  Domain: $[ - 1 , \infty )$
Range: $[ - 6 , \infty )$ 
C)  Domain: $( - \infty , \infty )$
Range: $[- \infty , -\ 6] $ 
D)  Domain: $( - \infty , \infty )$ 
Range: $[- \ 1 , \infty ] $

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

Divide using long division. - $\frac { 4 x ^ { 3 } - 43 x + 21 } { x - 3 }$

Find an nth degree polynomial function with real coefficients satisfying the given conditions. - $\mathrm { n } = 3 ; - 4$ and $\mathrm { i }$ are zeros; $\mathrm { f } ( - 3 ) = 60$

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

Divide using long division. - $\frac { 8 m ^ { 3 } + 44 m ^ { 2 } - 15 m + 54 } { m + 6 }$

Solve the polynomial equation. In order to obtain the first root, use synthetic division to test the possible rational roots. - $x ^ { 3 } - 5 x ^ { 2 } + 6 x - 2 = 0$

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

Find the x-intercepts (if any) for the graph of the quadratic function. - $f ( x ) = 2 x ^ { 2 } - 5 x - 3$

Solve the polynomial equation. In order to obtain the first root, use synthetic division to test the possible rational roots. - $3 \mathrm { x } ^ { 3 } - \mathrm { x } ^ { 2 } - 15 \mathrm { x } + 5 = 0$

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

Find the x-intercepts (if any) for the graph of the quadratic function. - $f ( x ) = x ^ { 2 } + 12 x + 15$ Give your answers in exact form.

Use the Intermediate Value Theorem to determine whether the polynomial function has a real zero between the given integers. - $f ( x ) = - 3 x ^ { 4 } - 4 x ^ { 3 } + 9 x + 3 ;$ between 1 and 2

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = - 3 x ^ { 2 } + 6 x + 1$

Solve the problem. -A rectangular playground is to be fenced off and divided in two by another fence parallel to one side of the playground. 624 feet of fencing is used. Find the maximum area of the playground.

Determine whether the function is a polynomial function. - $7 x ^ { 4 } - 3 x ^ { 3 } - 4 x - 2 y ^ { 5 } + 5$

x Find the range of the quadratic function. - $f ( x ) = 7 - ( x + 2 ) ^ { 2 }$

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 minimum is $- 6$ at $x = - 1$ .

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

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

Divide using long division. - 4x3−43x+21x−3\frac { 4 x ^ { 3 } - 43 x + 21 } { x - 3 }x−34x3−43x+21​

Find an nth degree polynomial function with real coefficients satisfying the given conditions. - n=3;−4\mathrm { n } = 3 ; - 4n=3;−4 and i\mathrm { i }i are zeros; f(−3)=60\mathrm { f } ( - 3 ) = 60f(−3)=60

Graph the rational function. - f(x)=2xx2−9f(x)=\frac{2 x}{x^{2}-9}f(x)=x2−92x​

Divide using long division. - 8m3+44m2−15m+54m+6\frac { 8 m ^ { 3 } + 44 m ^ { 2 } - 15 m + 54 } { m + 6 }m+68m3+44m2−15m+54​

Solve the polynomial equation. In order to obtain the first root, use synthetic division to test the possible rational roots. - x3−5x2+6x−2=0x ^ { 3 } - 5 x ^ { 2 } + 6 x - 2 = 0x3−5x2+6x−2=0

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

Find the x-intercepts (if any) for the graph of the quadratic function. - f(x)=2x2−5x−3f ( x ) = 2 x ^ { 2 } - 5 x - 3f(x)=2x2−5x−3

Solve the polynomial equation. In order to obtain the first root, use synthetic division to test the possible rational roots. - 3x3−x2−15x+5=03 \mathrm { x } ^ { 3 } - \mathrm { x } ^ { 2 } - 15 \mathrm { x } + 5 = 03x3−x2−15x+5=0

Graph the polynomial function. - f(x)=4x4+4x3f(x)=4 x^{4}+4 x^{3}f(x)=4x4+4x3

Find the x-intercepts (if any) for the graph of the quadratic function. - f(x)=x2+12x+15f ( x ) = x ^ { 2 } + 12 x + 15f(x)=x2+12x+15 Give your answers in exact form.

Use the Intermediate Value Theorem to determine whether the polynomial function has a real zero between the given integers. - f(x)=−3x4−4x3+9x+3;f ( x ) = - 3 x ^ { 4 } - 4 x ^ { 3 } + 9 x + 3 ;f(x)=−3x4−4x3+9x+3; between 1 and 2

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - f(x)=−3x2+6x+1f ( x ) = - 3 x ^ { 2 } + 6 x + 1f(x)=−3x2+6x+1

Solve the problem. -A rectangular playground is to be fenced off and divided in two by another fence parallel to one side of the playground. 624 feet of fencing is used. Find the maximum area of the playground.

Determine whether the function is a polynomial function. - 7x4−3x3−4x−2y5+57 x ^ { 4 } - 3 x ^ { 3 } - 4 x - 2 y ^ { 5 } + 57x4−3x3−4x−2y5+5

x Find the range of the quadratic function. - f(x)=7−(x+2)2f ( x ) = 7 - ( x + 2 ) ^ { 2 }f(x)=7−(x+2)2

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 minimum is −6- 6−6 at x=−1x = - 1x=−1 .

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

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

Divide using long division. - $\frac { 4 x ^ { 3 } - 43 x + 21 } { x - 3 }$

Find an nth degree polynomial function with real coefficients satisfying the given conditions. - $\mathrm { n } = 3 ; - 4$ and $\mathrm { i }$ are zeros; $\mathrm { f } ( - 3 ) = 60$

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

Divide using long division. - $\frac { 8 m ^ { 3 } + 44 m ^ { 2 } - 15 m + 54 } { m + 6 }$

Solve the polynomial equation. In order to obtain the first root, use synthetic division to test the possible rational roots. - $x ^ { 3 } - 5 x ^ { 2 } + 6 x - 2 = 0$

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

Find the x-intercepts (if any) for the graph of the quadratic function. - $f ( x ) = 2 x ^ { 2 } - 5 x - 3$

Solve the polynomial equation. In order to obtain the first root, use synthetic division to test the possible rational roots. - $3 \mathrm { x } ^ { 3 } - \mathrm { x } ^ { 2 } - 15 \mathrm { x } + 5 = 0$

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

Find the x-intercepts (if any) for the graph of the quadratic function. - $f ( x ) = x ^ { 2 } + 12 x + 15$ Give your answers in exact form.

Use the Intermediate Value Theorem to determine whether the polynomial function has a real zero between the given integers. - $f ( x ) = - 3 x ^ { 4 } - 4 x ^ { 3 } + 9 x + 3 ;$ between 1 and 2

Find the coordinates of the vertex for the parabola defined by the given quadratic function. - $f ( x ) = - 3 x ^ { 2 } + 6 x + 1$

Determine whether the function is a polynomial function. - $7 x ^ { 4 } - 3 x ^ { 3 } - 4 x - 2 y ^ { 5 } + 5$

x Find the range of the quadratic function. - $f ( x ) = 7 - ( x + 2 ) ^ { 2 }$

Find the domain and range of the quadratic function whose graph is described. -The minimum is $- 6$ at $x = - 1$ .