Question 1

Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval
notation.
-$$( 3 z + 10 ) ( 3 z - 1 ) > 0$$

Accepted Answer

A)  $\left( - \infty , - \frac { 10 } { 3 } \right) \cup \left( \frac { 1 } { 3 } , \infty \right)$
  
B)  $\left( \frac { 1 } { 3 } , \infty \right)$
  
C)  $\left( - \frac { 10 } { 3 } , \frac { 1 } { 3 } \right)$
  
D)  $\left[ - \frac { 10 } { 3 } , \frac { 1 } { 3 } \right]$
  
A)  $\left( - \infty , - \frac { 10 } { 3 } \right) \cup \left( \frac { 1 } { 3 } , \infty \right)$
  
B)  $\left( \frac { 1 } { 3 } , \infty \right)$
  
C)  $\left( - \frac { 10 } { 3 } , \frac { 1 } { 3 } \right)$
  
D)  $\left[ - \frac { 10 } { 3 } , \frac { 1 } { 3 } \right]$

Question 2

Solve the problem.
-A person standing close to the edge on top of a 320-foot building throws a baseball vertically upward. The quadratic function s(t) = -16t2 + 64t + 320 models the ball's height above the ground, s(t), in feet, t seconds after it was thrown. After how many seconds does the ball reach its maximum height? Round to the nearest tenth of a second if necessary.

Accepted Answer

A)  2 seconds 
B)  6.9 seconds 
C)  384 seconds 
D)  1.5 seconds 
A)  2 seconds 
B)  6.9 seconds 
C)  384 seconds 
D)  1.5 seconds

Question 3

Use the graph of the rational function shown to complete the statement.
- 
As $\mathrm { x } \rightarrow - 3 ^ { + } , \mathrm { f } ( \mathrm { x } ) \rightarrow$ ?

Accepted Answer

A)  $+ \infty$ 
B)  $- \infty$ 
C)  0 
D)  $- 3$ 
A)  $+ \infty$ 
B)  $- \infty$ 
C)  0 
D)  $- 3$

Question 4

Solve Combined Variation Problems
-$r$ varies directly as the square of $s$ and inversely as $t$.

Accepted Answer

A)  $\mathrm { r } = \frac { \mathrm { ks } ^ { 2 } } { \mathrm { t } }$ 
B)  $r = \frac { k t } { s ^ { 2 } }$ 
C)  $\mathrm { r } = \mathrm { k } + \mathrm { s } ^ { 2 } - \mathrm { t } ^ { 2 }$ 
D)  $\mathrm { r } = \mathrm { ks } ^ { 2 }$ 
A)  $\mathrm { r } = \frac { \mathrm { ks } ^ { 2 } } { \mathrm { t } }$ 
B)  $r = \frac { k t } { s ^ { 2 } }$ 
C)  $\mathrm { r } = \mathrm { k } + \mathrm { s } ^ { 2 } - \mathrm { t } ^ { 2 }$ 
D)  $\mathrm { r } = \mathrm { ks } ^ { 2 }$

Question 5

Use the Rational Zero Theorem to list all possible rational zeros for the given function.
-$$f ( x ) = - 2 x ^ { 3 } + 2 x ^ { 2 } - 4 x + 8$$

Accepted Answer

A)  $\pm \frac { 1 } { 2 } , \pm 1 , \pm 2 , \pm 4 , \pm 8$ 
B)  $\pm \frac { 1 } { 4 } , \pm \frac { 1 } { 2 } , \pm 1 , \pm 2 , \pm 4 , \pm 8$ 
C)  $\pm \frac { 1 } { 8 } , \pm \frac { 1 } { 4 } , \pm \frac { 1 } { 2 } , \pm 1 , \pm 2 , \pm 4 , \pm 8$ 
D)  $\pm \frac { 1 } { 2 } , \pm 1 , \pm 2 , \pm 4$ 
A)  $\pm \frac { 1 } { 2 } , \pm 1 , \pm 2 , \pm 4 , \pm 8$ 
B)  $\pm \frac { 1 } { 4 } , \pm \frac { 1 } { 2 } , \pm 1 , \pm 2 , \pm 4 , \pm 8$ 
C)  $\pm \frac { 1 } { 8 } , \pm \frac { 1 } { 4 } , \pm \frac { 1 } { 2 } , \pm 1 , \pm 2 , \pm 4 , \pm 8$ 
D)  $\pm \frac { 1 } { 2 } , \pm 1 , \pm 2 , \pm 4$

Question 6

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. Then use this end
-$$f ( x ) = ( x - 1 ) ( x + 1 ) ( x + 3 ) ^ { 3 }$$

Accepted Answer

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

Question 7

Use the graph of the rational function shown to complete the statement.
-

As $\mathrm { x } \rightarrow 2 ^ { + } , \mathrm { f } ( \mathrm { x } ) \rightarrow$ ?

Accepted Answer

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

Question 8

Solve the rational inequality and graph the solution set on a real number line. Express the solution set in interval
notation.
-$$\frac { ( x + 5 ) ( x - 2 ) } { x - 1 } \geq 0$$

Accepted Answer

A)  $[ - 5,1 ) \cup [ 2 , \infty )$
  
B)  $( - \infty , - 5 ] \cup ( 1,2 ]$
  
C)  $( - \infty , - 5 ] \cup [ 2 , \infty )$
  
D)  $[ - 5,1 ] \cup [ 2 , \infty )$
  
A)  $[ - 5,1 ) \cup [ 2 , \infty )$
  
B)  $( - \infty , - 5 ] \cup ( 1,2 ]$
  
C)  $( - \infty , - 5 ] \cup [ 2 , \infty )$
  
D)  $[ - 5,1 ] \cup [ 2 , \infty )$

Question 9

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

Accepted Answer

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

Question 10

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

Accepted Answer

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

Question 11

Find the slant asymptote, if any, of the graph of the rational function.
-$$f ( x ) = \frac { x ^ { 2 } + 16 } { x }$$

Accepted Answer

A)  $y = x$ 
B)  $y = x + 16$ 
C)  $x = 0$ 
D)  no slant asymptote 
A)  $y = x$ 
B)  $y = x + 16$ 
C)  $x = 0$ 
D)  no slant asymptote

Question 12

Graph the polynomial function.
-$f(x)=x^{5}-3 x^{3}-18 x$

Accepted Answer

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

Question 13

Find a rational zero of the polynomial function and use it to find all the zeros of the function.
-$$f ( x ) = x ^ { 3 } - 8 x ^ { 2 } + 14 x - 4$$

Accepted Answer

A)  $\{ 2,3 + \sqrt { 7 } , 3 - \sqrt { 7 } \}$ 
B)  $\{ 1 , - 1,4 \}$ 
C)  $\{ - 2,6 + \sqrt { 7 } , 6 - \sqrt { 7 } \}$ 
D)  $\{ 2,6 + \sqrt { 4 } , 6 - \sqrt { 4 } \}$ 
A)  $\{ 2,3 + \sqrt { 7 } , 3 - \sqrt { 7 } \}$ 
B)  $\{ 1 , - 1,4 \}$ 
C)  $\{ - 2,6 + \sqrt { 7 } , 6 - \sqrt { 7 } \}$ 
D)  $\{ 2,6 + \sqrt { 4 } , 6 - \sqrt { 4 } \}$

Question 14

Solve the polynomial equation. In order to obtain the first root, use synthetic division to test the possible rational
roots.
-$$x ^ { 4 } - 3 x ^ { 3 } - 2 x ^ { 2 } + 32 x - 48 = 0$$

Accepted Answer

A)  $\{ - 3,2,2 + 2 i , 2 - 2 i \}$ 
B)  $\{ 3 , - 2,2 + 2 i , 2 - 2 i \}$ 
C)  $\{ - 3,2,2 + 3 i , 2 - 3 i \}$ 
D)  $\{ 3 , - 2,2 + \sqrt { 2 } , 2 - \sqrt { 2 } \}$ 
A)  $\{ - 3,2,2 + 2 i , 2 - 2 i \}$ 
B)  $\{ 3 , - 2,2 + 2 i , 2 - 2 i \}$ 
C)  $\{ - 3,2,2 + 3 i , 2 - 3 i \}$ 
D)  $\{ 3 , - 2,2 + \sqrt { 2 } , 2 - \sqrt { 2 } \}$

Question 15

Solve the polynomial equation. In order to obtain the first root, use synthetic division to test the possible rational
roots.
-The polynomial function
$$\mathrm { H } ( \mathrm { x } ) = - 0.001183 \mathrm { x } ^ { 4 } + 0.05495 \mathrm { x } ^ { 3 } - 0.8523 \mathrm { x } ^ { 2 } + 9.054 \mathrm { x } + 6.748$$
models the age in human years, $\mathrm { H } ( \mathrm { x } )$, of a dog that is $x$ years old, where $x \geq 1$. Using the graph of this function shown below, what is the approximately equivalent dog age for a person who is 60 ?

Accepted Answer

A)  11 years 
B)  9 years 
C)  $8.5$ years 
D)  $12.5$ years 
A)  11 years 
B)  9 years 
C)  $8.5$ years 
D)  $12.5$ years

Question 16

Find the indicated intercept(s) of the graph of the function.
-Is there origin symmetry for the rational function $f ( x ) = \frac { 6 x ^ { 2 } + 18 } { 6 x }$ ?

Accepted Answer

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

Question 17

Graph the polynomial function.
-$f(x)=x^{4}+6 x^{3}+9 x^{2}$

Accepted Answer

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

Question 18

Find the indicated intercept(s) of the graph of the function.
-$x$-intercepts of $f ( x ) = \frac { x ^ { 2 } + 7 x } { x ^ { 2 } + 9 x - 3 }$

Accepted Answer

A)  $( 0,0 )$ and $( - 7,0 )$ 
B)  $( - 7,0 )$ 
C)  $( 0,0 )$ and $( 7,0 )$ 
D)  $( 7,0 )$ 
A)  $( 0,0 )$ and $( - 7,0 )$ 
B)  $( - 7,0 )$ 
C)  $( 0,0 )$ and $( 7,0 )$ 
D)  $( 7,0 )$

Question 19

Graph the polynomial function.
-$f(x)=-x^{2}(x+1)(x+4)$

Accepted Answer

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

Question 20

Determine the constant of variation for the stated condition.
-s varies directly as $r$, and $\mathrm { s } = 9$ when $\mathrm { r } = 117$.

Accepted Answer

A)  $\mathrm { k } = \frac { 1 } { 13 }$ 
B)  $\mathrm { k } = 12$ 
C)  $\mathrm { k } = 13$ 
D)  $\mathrm { k } = 108$ 
A)  $\mathrm { k } = \frac { 1 } { 13 }$ 
B)  $\mathrm { k } = 12$ 
C)  $\mathrm { k } = 13$ 
D)  $\mathrm { k } = 108$

Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation. - $( 3 z + 10 ) ( 3 z - 1 ) > 0$

Solve Combined Variation Problems - $r$ varies directly as the square of $s$ and inversely as $t$ .

Use the Rational Zero Theorem to list all possible rational zeros for the given function. - $f ( x ) = - 2 x ^ { 3 } + 2 x ^ { 2 } - 4 x + 8$

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. Then use this end - $f ( x ) = ( x - 1 ) ( x + 1 ) ( x + 3 ) ^ { 3 }$

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

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

Find the slant asymptote, if any, of the graph of the rational function. - $f ( x ) = \frac { x ^ { 2 } + 16 } { x }$

Graph the polynomial function. - $f(x)=x^{5}-3 x^{3}-18 x$ $Graph the polynomial function. - f(x)=x^{5}-3 x^{3}-18 x$

Find a rational zero of the polynomial function and use it to find all the zeros of the function. - $f ( x ) = x ^ { 3 } - 8 x ^ { 2 } + 14 x - 4$

Solve the polynomial equation. In order to obtain the first root, use synthetic division to test the possible rational roots. - $x ^ { 4 } - 3 x ^ { 3 } - 2 x ^ { 2 } + 32 x - 48 = 0$

Find the indicated intercept(s) of the graph of the function. -Is there origin symmetry for the rational function $f ( x ) = \frac { 6 x ^ { 2 } + 18 } { 6 x }$ ?

Graph the polynomial function. - $f(x)=x^{4}+6 x^{3}+9 x^{2}$ $Graph the polynomial function. - f(x)=x^{4}+6 x^{3}+9 x^{2}$

Find the indicated intercept(s) of the graph of the function. - $x$ -intercepts of $f ( x ) = \frac { x ^ { 2 } + 7 x } { x ^ { 2 } + 9 x - 3 }$

Graph the polynomial function. - $f(x)=-x^{2}(x+1)(x+4)$ $Graph the polynomial function. - f(x)=-x^{2}(x+1)(x+4)$

Determine the constant of variation for the stated condition. -s varies directly as $r$ , and $\mathrm { s } = 9$ when $\mathrm { r } = 117$ .

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

Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation. - (3z+10)(3z−1)>0( 3 z + 10 ) ( 3 z - 1 ) > 0(3z+10)(3z−1)>0

Use the graph of the rational function shown to complete the statement. - As x→−3+,f(x)→\mathrm { x } \rightarrow - 3 ^ { + } , \mathrm { f } ( \mathrm { x } ) \rightarrowx→−3+,f(x)→ ?

Solve Combined Variation Problems - rrr varies directly as the square of sss and inversely as ttt .

Use the Rational Zero Theorem to list all possible rational zeros for the given function. - f(x)=−2x3+2x2−4x+8f ( x ) = - 2 x ^ { 3 } + 2 x ^ { 2 } - 4 x + 8f(x)=−2x3+2x2−4x+8

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. Then use this end - f(x)=(x−1)(x+1)(x+3)3f ( x ) = ( x - 1 ) ( x + 1 ) ( x + 3 ) ^ { 3 }f(x)=(x−1)(x+1)(x+3)3

Use the graph of the rational function shown to complete the statement. - As x→2+,f(x)→\mathrm { x } \rightarrow 2 ^ { + } , \mathrm { f } ( \mathrm { x } ) \rightarrowx→2+,f(x)→ ?

Solve the rational inequality and graph the solution set on a real number line. Express the solution set in interval notation. - (x+5)(x−2)x−1≥0\frac { ( x + 5 ) ( x - 2 ) } { x - 1 } \geq 0x−1(x+5)(x−2)​≥0

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

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

Find the slant asymptote, if any, of the graph of the rational function. - f(x)=x2+16xf ( x ) = \frac { x ^ { 2 } + 16 } { x }f(x)=xx2+16​

Graph the polynomial function. - f(x)=x5−3x3−18xf(x)=x^{5}-3 x^{3}-18 xf(x)=x5−3x3−18x

Find a rational zero of the polynomial function and use it to find all the zeros of the function. - f(x)=x3−8x2+14x−4f ( x ) = x ^ { 3 } - 8 x ^ { 2 } + 14 x - 4f(x)=x3−8x2+14x−4

Solve the polynomial equation. In order to obtain the first root, use synthetic division to test the possible rational roots. - x4−3x3−2x2+32x−48=0x ^ { 4 } - 3 x ^ { 3 } - 2 x ^ { 2 } + 32 x - 48 = 0x4−3x3−2x2+32x−48=0

Find the indicated intercept(s) of the graph of the function. -Is there origin symmetry for the rational function f(x)=6x2+186xf ( x ) = \frac { 6 x ^ { 2 } + 18 } { 6 x }f(x)=6x6x2+18​ ?

Graph the polynomial function. - f(x)=x4+6x3+9x2f(x)=x^{4}+6 x^{3}+9 x^{2}f(x)=x4+6x3+9x2

Find the indicated intercept(s) of the graph of the function. - xxx -intercepts of f(x)=x2+7xx2+9x−3f ( x ) = \frac { x ^ { 2 } + 7 x } { x ^ { 2 } + 9 x - 3 }f(x)=x2+9x−3x2+7x​

Graph the polynomial function. - f(x)=−x2(x+1)(x+4)f(x)=-x^{2}(x+1)(x+4)f(x)=−x2(x+1)(x+4)

Determine the constant of variation for the stated condition. -s varies directly as rrr , and s=9\mathrm { s } = 9s=9 when r=117\mathrm { r } = 117r=117 .

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

Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation. - $( 3 z + 10 ) ( 3 z - 1 ) > 0$

Solve Combined Variation Problems - $r$ varies directly as the square of $s$ and inversely as $t$ .

Use the Rational Zero Theorem to list all possible rational zeros for the given function. - $f ( x ) = - 2 x ^ { 3 } + 2 x ^ { 2 } - 4 x + 8$

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. Then use this end - $f ( x ) = ( x - 1 ) ( x + 1 ) ( x + 3 ) ^ { 3 }$

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

Find the slant asymptote, if any, of the graph of the rational function. - $f ( x ) = \frac { x ^ { 2 } + 16 } { x }$

Graph the polynomial function. - $f(x)=x^{5}-3 x^{3}-18 x$ $Graph the polynomial function. - f(x)=x^{5}-3 x^{3}-18 x$

Find a rational zero of the polynomial function and use it to find all the zeros of the function. - $f ( x ) = x ^ { 3 } - 8 x ^ { 2 } + 14 x - 4$

Solve the polynomial equation. In order to obtain the first root, use synthetic division to test the possible rational roots. - $x ^ { 4 } - 3 x ^ { 3 } - 2 x ^ { 2 } + 32 x - 48 = 0$

Find the indicated intercept(s) of the graph of the function. -Is there origin symmetry for the rational function $f ( x ) = \frac { 6 x ^ { 2 } + 18 } { 6 x }$ ?

Graph the polynomial function. - $f(x)=x^{4}+6 x^{3}+9 x^{2}$ $Graph the polynomial function. - f(x)=x^{4}+6 x^{3}+9 x^{2}$

Find the indicated intercept(s) of the graph of the function. - $x$ -intercepts of $f ( x ) = \frac { x ^ { 2 } + 7 x } { x ^ { 2 } + 9 x - 3 }$

Graph the polynomial function. - $f(x)=-x^{2}(x+1)(x+4)$ $Graph the polynomial function. - f(x)=-x^{2}(x+1)(x+4)$

Determine the constant of variation for the stated condition. -s varies directly as $r$ , and $\mathrm { s } = 9$ when $\mathrm { r } = 117$ .