Question 1

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. Then use this end
-$$f ( x ) = - x ^ { 2 } ( x - 4 ) ( x + 2 )$$

Accepted Answer

A)  falls to the left and falls to the right 
B)  falls to the left and rises to the right 
C)  rises to the left and falls to the right 
D)  rises to the left and rises to the right 
A)  falls to the left and falls to the right 
B)  falls to the left and rises to the right 
C)  rises to the left and falls to the right 
D)  rises to the left and rises to the right

Question 2

Find the axis of symmetry of the parabola defined by the given quadratic function.
-$$f ( x ) = 4 - ( x + 5 ) ^ { 2 }$$

Accepted Answer

A)  $x = - 5$ 
B)  $x = 5$ 
C)  $x = 4$ 
D)  $x = - 4$ x 
A)  $x = - 5$ 
B)  $x = 5$ 
C)  $x = 4$ 
D)  $x = - 4$ x

Question 3

Graph the polynomial function.
-$f(x)=x^{4}+14 x^{3}+49 x^{2}$

Accepted Answer

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

Question 4

Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval
notation.
-$$x ^ { 2 } - 3 x - 28 < 0$$

Accepted Answer

A)  $( - 4,7 )$
  
B)  $( - \infty , - 4 )$
  
C)  $( 7 , \infty )$
  
D)  $( - \infty , - 4 ) \cup ( 7 , \infty )$
  
A)  $( - 4,7 )$
  
B)  $( - \infty , - 4 )$
  
C)  $( 7 , \infty )$
  
D)  $( - \infty , - 4 ) \cup ( 7 , \infty )$

Question 5

Use the graph of the rational function shown to complete the statement.
- 
As $x \rightarrow 0 ^ { - } , f ( x ) \rightarrow$ ?

Accepted Answer

A)  $- \infty$ 
B)  $+ \infty$ 
C)  2 
D)  0 
A)  $- \infty$ 
B)  $+ \infty$ 
C)  2 
D)  0

Question 6

Find the y-intercept of the polynomial function.
-$$f ( x ) = - x ^ { 2 } ( x + 4 ) ( x - 7 )$$

Accepted Answer

A)  0 
B)  $- 7$ 
C)  $- 28$ 
D)  28 
A)  0 
B)  $- 7$ 
C)  $- 28$ 
D)  28

Question 7

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.
-$f(x)=10+7 x+x^{2}$

Accepted Answer

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

Question 8

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 9

Solve the problem.
-The owner of a video store has determined that the cost $C$, in dollars, of operating the store is approximately given by $C ( x ) = 2 x ^ { 2 } - 26 x + 640$, where $x$ is the number of videos rented daily. Find the lowest cost to the nearest dollar.

Accepted Answer

A)  $\$ 556$ 
B)  $\$ 302$ 
C)  $\$ 471$ 
D)  $\$ 725$ 
A)  $\$ 556$ 
B)  $\$ 302$ 
C)  $\$ 471$ 
D)  $\$ 725$

Question 10

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

Accepted Answer

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

Question 11

Divide using long division.
-$\left( 15 x ^ { 2 } - 61 x + 56 \right) \div ( - 5 x + 7 )$

Accepted Answer

A)  $- 3 x + 8$ 
B)  $15 x + 8$ 
C)  $x + 8$ 
D)  $8 x + 1$ 8x 
A)  $- 3 x + 8$ 
B)  $15 x + 8$ 
C)  $x + 8$ 
D)  $8 x + 1$ 8x

Question 12

Solve the problem.
-You have 84 feet of fencing to enclose a rectangular plot that borders on a river. If you do not fence the side along the river, find the length and width of the plot that will maximize the area.

Accepted Answer

A)  length: 42 feet, width: 21 feet 
B)  length: 63 feet, width: 21 feet 
C)  length: 42 feet, width: 42 feet 
D)  length: 21 feet, width: 21 feet 
A)  length: 42 feet, width: 21 feet 
B)  length: 63 feet, width: 21 feet 
C)  length: 42 feet, width: 42 feet 
D)  length: 21 feet, width: 21 feet

Question 13

Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval
notation.
-$$3 x ^ { 2 } - 5 x \geq 8$$

Accepted Answer

A)  $( - \infty , - 1 ] \cup \left[ \frac { 8 } { 3 } , \infty \right)$
  
B)  $( - \infty , - 1 ) \cup \left( \frac { 8 } { 3 } , \infty \right)$
  
C)  $\left[ - 1 , \frac { 8 } { 3 } \right]$
  
D)  $\left( - 1 , \frac { 8 } { 3 } \right)$
  
A)  $( - \infty , - 1 ] \cup \left[ \frac { 8 } { 3 } , \infty \right)$
  
B)  $( - \infty , - 1 ) \cup \left( \frac { 8 } { 3 } , \infty \right)$
  
C)  $\left[ - 1 , \frac { 8 } { 3 } \right]$
  
D)  $\left( - 1 , \frac { 8 } { 3 } \right)$

Question 14

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

Accepted Answer

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

Question 15

Use the Intermediate Value Theorem to determine whether the polynomial function has a real zero between the
given integers.
-$f ( x ) = 6 x ^ { 3 } - 9 x ^ { 2 } - 6 x + 8$; between 1 and 2

Accepted Answer

A)  $f ( 1 ) = - 1$ and $f ( 2 ) = 8$; yes 
B)  $f ( 1 ) = 1$ and $f ( 2 ) = 8$; no 
C)  $f ( 1 ) = - 1$ and $f ( 2 ) = - 8$; no 
D)  $f ( 1 ) = 1$ and $f ( 2 ) = - 8$; yes 
A)  $f ( 1 ) = - 1$ and $f ( 2 ) = 8$; yes 
B)  $f ( 1 ) = 1$ and $f ( 2 ) = 8$; no 
C)  $f ( 1 ) = - 1$ and $f ( 2 ) = - 8$; no 
D)  $f ( 1 ) = 1$ and $f ( 2 ) = - 8$; yes

Question 16

Solve Combined Variation Problems
-$P$ varies jointly as $R$ and $S$ and inversely as the square root of $a$.

Accepted Answer

A)  $\mathrm { P } = \frac { \mathrm { kRS } } { \sqrt { \mathrm { a } } }$ 
B)  $P = \frac { k R } { S \sqrt { a } }$ 
C)  $\mathrm { P } = \frac { \mathrm { k } ( \mathrm { R } + \mathrm { S } ) } { \sqrt { \mathrm { a } } }$ 
D)  $P = \frac { R S } { k \sqrt { a } }$ 
A)  $\mathrm { P } = \frac { \mathrm { kRS } } { \sqrt { \mathrm { a } } }$ 
B)  $P = \frac { k R } { S \sqrt { a } }$ 
C)  $\mathrm { P } = \frac { \mathrm { k } ( \mathrm { R } + \mathrm { S } ) } { \sqrt { \mathrm { a } } }$ 
D)  $P = \frac { R S } { k \sqrt { a } }$

Question 17

Use synthetic division and the Remainder Theorem to find the indicated function value.
-$$f ( x ) = 2 x ^ { 3 } - 7 x ^ { 2 } - 5 x + 12 ; f ( - 3 )$$

Accepted Answer

A)  $- 90$ 
B)  $- 18$ 
C)  54 
D)  $- 120$ 
A)  $- 90$ 
B)  $- 18$ 
C)  54 
D)  $- 120$

Question 18

Determine whether the function is a polynomial function.
-$$f ( x ) = \frac { 8 - x ^ { 2 } } { 2 }$$

Accepted Answer

A)  $Y e s$ 
B)  No 
A)  $Y e s$ 
B)  No

Question 19

Find the domain and range of the quadratic function whose graph is described.
-Write an equation in standard form of the parabola that has the same shape as the graph of $f ( x ) = - 7 x ^ { 2 }$, but which has a maximum of 8 at $x = 4$.

Accepted Answer

A)  $f ( x ) = - 7 ( x - 4 ) ^ { 2 } + 8$ 
B)  $f ( x ) = - 7 ( x + 4 ) ^ { 2 } + 8$ 
C)  $f ( x ) = 7 ( x - 4 ) ^ { 2 } + 8$ 
D)  $f ( x ) = - 7 ( x - 4 ) ^ { 2 } - 8$ 
A)  $f ( x ) = - 7 ( x - 4 ) ^ { 2 } + 8$ 
B)  $f ( x ) = - 7 ( x + 4 ) ^ { 2 } + 8$ 
C)  $f ( x ) = 7 ( x - 4 ) ^ { 2 } + 8$ 
D)  $f ( x ) = - 7 ( x - 4 ) ^ { 2 } - 8$

Question 20

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

Accepted Answer

A)  $x = 2$ 
B)  $x = 0$ and $x = 2$ 
C)  $x = 0$ and $x = - 2$ 
D)  no vertical asymptote 
A)  $x = 2$ 
B)  $x = 0$ and $x = 2$ 
C)  $x = 0$ and $x = - 2$ 
D)  no vertical asymptote

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. Then use this end - $f ( x ) = - x ^ { 2 } ( x - 4 ) ( x + 2 )$

Find the axis of symmetry of the parabola defined by the given quadratic function. - $f ( x ) = 4 - ( x + 5 ) ^ { 2 }$

Graph the polynomial function. - $f(x)=x^{4}+14 x^{3}+49 x^{2}$ $Graph the polynomial function. - f(x)=x^{4}+14 x^{3}+49 x^{2}$

Use the graph of the rational function shown to complete the statement. - $Use the graph of the rational function shown to complete the statement. - As x \rightarrow 0 ^ { - } , f ( x ) \rightarrow ?$ As $x \rightarrow 0 ^ { - } , f ( x ) \rightarrow$ ?

Find the y-intercept of the polynomial function. - $f ( x ) = - x ^ { 2 } ( x + 4 ) ( x - 7 )$

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

Solve the problem. -The owner of a video store has determined that the cost $C$ , in dollars, of operating the store is approximately given by $C ( x ) = 2 x ^ { 2 } - 26 x + 640$ , where $x$ is the number of videos rented daily. Find the lowest cost to the nearest dollar.

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

Divide using long division. - $\left( 15 x ^ { 2 } - 61 x + 56 \right) \div ( - 5 x + 7 )$

Solve the problem. -You have 84 feet of fencing to enclose a rectangular plot that borders on a river. If you do not fence the side along the river, find the length and width of the plot that will maximize the area.

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

Use the Intermediate Value Theorem to determine whether the polynomial function has a real zero between the given integers. - $f ( x ) = 6 x ^ { 3 } - 9 x ^ { 2 } - 6 x + 8$ ; between 1 and 2

Solve Combined Variation Problems - $P$ varies jointly as $R$ and $S$ and inversely as the square root of $a$ .

Use synthetic division and the Remainder Theorem to find the indicated function value. - $f ( x ) = 2 x ^ { 3 } - 7 x ^ { 2 } - 5 x + 12 ; f ( - 3 )$

Determine whether the function is a polynomial function. - $f ( x ) = \frac { 8 - x ^ { 2 } } { 2 }$

Find the domain and range of the quadratic function whose graph is described. -Write an equation in standard form of the parabola that has the same shape as the graph of $f ( x ) = - 7 x ^ { 2 }$ , but which has a maximum of 8 at $x = 4$ .

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

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 Leading Coefficient Test to determine the end behavior of the polynomial function. Then use this end - f(x)=−x2(x−4)(x+2)f ( x ) = - x ^ { 2 } ( x - 4 ) ( x + 2 )f(x)=−x2(x−4)(x+2)

Find the axis of symmetry of the parabola defined by the given quadratic function. - f(x)=4−(x+5)2f ( x ) = 4 - ( x + 5 ) ^ { 2 }f(x)=4−(x+5)2

Graph the polynomial function. - f(x)=x4+14x3+49x2f(x)=x^{4}+14 x^{3}+49 x^{2}f(x)=x4+14x3+49x2

Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation. - x2−3x−28<0x ^ { 2 } - 3 x - 28 < 0x2−3x−28<0

Use the graph of the rational function shown to complete the statement. - As x→0−,f(x)→x \rightarrow 0 ^ { - } , f ( x ) \rightarrowx→0−,f(x)→ ?

Find the y-intercept of the polynomial function. - f(x)=−x2(x+4)(x−7)f ( x ) = - x ^ { 2 } ( x + 4 ) ( x - 7 )f(x)=−x2(x+4)(x−7)

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)=10+7x+x2f(x)=10+7 x+x^{2}f(x)=10+7x+x2

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

Graph the polynomial function. - f(x)=x4−3x3−x2+3f ( x ) = x ^ { 4 } - 3 x ^ { 3 } - x ^ { 2 } + 3f(x)=x4−3x3−x2+3

Divide using long division. - (15x2−61x+56)÷(−5x+7)\left( 15 x ^ { 2 } - 61 x + 56 \right) \div ( - 5 x + 7 )(15x2−61x+56)÷(−5x+7)

Solve the problem. -You have 84 feet of fencing to enclose a rectangular plot that borders on a river. If you do not fence the side along the river, find the length and width of the plot that will maximize the area.

Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation. - 3x2−5x≥83 x ^ { 2 } - 5 x \geq 83x2−5x≥8

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

Use the Intermediate Value Theorem to determine whether the polynomial function has a real zero between the given integers. - f(x)=6x3−9x2−6x+8f ( x ) = 6 x ^ { 3 } - 9 x ^ { 2 } - 6 x + 8f(x)=6x3−9x2−6x+8 ; between 1 and 2

Solve Combined Variation Problems - PPP varies jointly as RRR and SSS and inversely as the square root of aaa .

Use synthetic division and the Remainder Theorem to find the indicated function value. - f(x)=2x3−7x2−5x+12;f(−3)f ( x ) = 2 x ^ { 3 } - 7 x ^ { 2 } - 5 x + 12 ; f ( - 3 )f(x)=2x3−7x2−5x+12;f(−3)

Determine whether the function is a polynomial function. - f(x)=8−x22f ( x ) = \frac { 8 - x ^ { 2 } } { 2 }f(x)=28−x2​

Find the domain and range of the quadratic function whose graph is described. -Write an equation in standard form of the parabola that has the same shape as the graph of f(x)=−7x2f ( x ) = - 7 x ^ { 2 }f(x)=−7x2 , but which has a maximum of 8 at x=4x = 4x=4 .

Find the vertical asymptotes, if any, of the graph of the rational function. - f(x)=xx(x−2)f ( x ) = \frac { x } { x ( x - 2 ) }f(x)=x(x−2)x​

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 Leading Coefficient Test to determine the end behavior of the polynomial function. Then use this end - $f ( x ) = - x ^ { 2 } ( x - 4 ) ( x + 2 )$

Find the axis of symmetry of the parabola defined by the given quadratic function. - $f ( x ) = 4 - ( x + 5 ) ^ { 2 }$

Graph the polynomial function. - $f(x)=x^{4}+14 x^{3}+49 x^{2}$ $Graph the polynomial function. - f(x)=x^{4}+14 x^{3}+49 x^{2}$

Use the graph of the rational function shown to complete the statement. - $Use the graph of the rational function shown to complete the statement. - As x \rightarrow 0 ^ { - } , f ( x ) \rightarrow ?$ As $x \rightarrow 0 ^ { - } , f ( x ) \rightarrow$ ?

Find the y-intercept of the polynomial function. - $f ( x ) = - x ^ { 2 } ( x + 4 ) ( x - 7 )$

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

Divide using long division. - $\left( 15 x ^ { 2 } - 61 x + 56 \right) \div ( - 5 x + 7 )$

Use the Intermediate Value Theorem to determine whether the polynomial function has a real zero between the given integers. - $f ( x ) = 6 x ^ { 3 } - 9 x ^ { 2 } - 6 x + 8$ ; between 1 and 2

Solve Combined Variation Problems - $P$ varies jointly as $R$ and $S$ and inversely as the square root of $a$ .

Use synthetic division and the Remainder Theorem to find the indicated function value. - $f ( x ) = 2 x ^ { 3 } - 7 x ^ { 2 } - 5 x + 12 ; f ( - 3 )$

Determine whether the function is a polynomial function. - $f ( x ) = \frac { 8 - x ^ { 2 } } { 2 }$

Find the domain and range of the quadratic function whose graph is described. -Write an equation in standard form of the parabola that has the same shape as the graph of $f ( x ) = - 7 x ^ { 2 }$ , but which has a maximum of 8 at $x = 4$ .

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