Question 1

Determine the constant of variation for the stated condition.
-f varies jointly as $q ^ { 2 }$ and $h$, and $f = 64$ when $q = 4$ and $h = 2$. Find $q$ when $f = 90$ and $h = 5$.

Accepted Answer

A)  $q = 3$ 
B)  $q = 2$ 
C)  $\mathrm { q } = 4$ 
D)  $q = 5$ q 
A)  $q = 3$ 
B)  $q = 2$ 
C)  $\mathrm { q } = 4$ 
D)  $q = 5$ q

Question 2

Find the x-intercepts (if any) for the graph of the quadratic function.
-$$f ( x ) = x ^ { 2 } - 4$$

Accepted Answer

A)  $( - 2,0 )$ and $( 2,0 )$ 
B)  $( - 4,0 )$ 
C)  $( 2,0 )$ 
D)  No x-intercepts 
A)  $( - 2,0 )$ and $( 2,0 )$ 
B)  $( - 4,0 )$ 
C)  $( 2,0 )$ 
D)  No x-intercepts

Question 3

Determine the constant of variation for the stated condition.
-$y = 0.4$ when $x = 0.8$

Accepted Answer

A)  $y = 0.5 x$ 
B)  $y = 0.4 x$ 
C)  $y = x - 0.4$ 
D)  $y = 2 x$ 
A)  $y = 0.5 x$ 
B)  $y = 0.4 x$ 
C)  $y = x - 0.4$ 
D)  $y = 2 x$

Question 4

Determine whether the function is a polynomial function.
-$$f ( x ) = 10 x ^ { 4 } + 7 x ^ { 3 } + 5$$

Accepted Answer

A)  4 
B)  8 
C)  7 
D)  10 
A)  4 
B)  8 
C)  7 
D)  10

Question 5

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

Accepted Answer

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

Question 6

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

Accepted Answer

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

Question 7

Determine the constant of variation for the stated condition.
-$c$ varies directly as $a$ and inversely as $b ; c = 5$ when $a = 65$ and $b = 117$

Accepted Answer

A)  $\mathrm { c } = \frac { 9 \mathrm { a } } { \mathrm { b } }$ 
B)  $c = \frac { a } { 9 b }$ 
C)  $c = 9 a b$ 
D)  $c = \frac { 9 } { a b }$ 
A)  $\mathrm { c } = \frac { 9 \mathrm { a } } { \mathrm { b } }$ 
B)  $c = \frac { a } { 9 b }$ 
C)  $c = 9 a b$ 
D)  $c = \frac { 9 } { a b }$

Question 8

Determine the maximum possible number of turning points for the graph of the function.
-$$f ( x ) = - x ^ { 2 } - 6 x + 5$$

Accepted Answer

A)  1 
B)  2 
C)  0 
D)  3 
A)  1 
B)  2 
C)  0 
D)  3

Question 9

Find the indicated intercept(s) of the graph of the function.
-Is there origin symmetry for the rational function $f ( x ) = \frac { - 4 x } { - 7 x ^ { 2 } + 13 }$ ?

Accepted Answer

A)  Yes 
B)  $\mathrm { No }$ 
A)  Yes 
B)  $\mathrm { No }$

Question 10

Divide using long division.
-$\frac { 10 t ^ { 4 } + 14 t ^ { 3 } - 25 t ^ { 2 } + 39 t - 30 } { 2 t ^ { 2 } + 4 t - 5 }$

Accepted Answer

A)  $5 t ^ { 2 } - 3 t + 6$ 
B)  $5 t ^ { 2 } + 3 t + 6$ 
C)  $5 t ^ { 2 } - 3 t - 6$ 
D)  $5 t ^ { 2 } - 2 t + 6$ 
A)  $5 t ^ { 2 } - 3 t + 6$ 
B)  $5 t ^ { 2 } + 3 t + 6$ 
C)  $5 t ^ { 2 } - 3 t - 6$ 
D)  $5 t ^ { 2 } - 2 t + 6$

Question 11

Solve the problem.
-Solve the equation $8 x ^ { 3 } - 42 x ^ { 2 } + 43 x - 12 = 0$ given that $\frac { 1 } { 2 }$ is a root.

Accepted Answer

A)  $\left\{ \frac { 1 } { 2 } , \frac { 3 } { 4 } , 4 \right\}$ 
B)  $\left\{ \frac { 1 } { 2 } , - \frac { 3 } { 4 } , - 4 \right\}$ 
C)  $\left\{ \frac { 1 } { 2 } , 1,3 \right\}$ 
D)  $\left\{ \frac { 1 } { 2 } , - 1 , - 3 \right\}$ 
A)  $\left\{ \frac { 1 } { 2 } , \frac { 3 } { 4 } , 4 \right\}$ 
B)  $\left\{ \frac { 1 } { 2 } , - \frac { 3 } { 4 } , - 4 \right\}$ 
C)  $\left\{ \frac { 1 } { 2 } , 1,3 \right\}$ 
D)  $\left\{ \frac { 1 } { 2 } , - 1 , - 3 \right\}$

Question 12

Determine whether the function is a polynomial function.
-$$f ( x ) = x ^ { 3 / 2 } - x ^ { 5 } + 2$$

Accepted Answer

A)  $\mathrm { No }$ 
B)  Yes 
A)  $\mathrm { No }$ 
B)  Yes

Question 13

Divide using long division.
-$$\left( 4 x ^ { 5 } - x ^ { 3 } + 3 x ^ { 2 } - 180 x - 21 \right) \div \left( x ^ { 2 } - 7 \right)$$

Accepted Answer

A)  $4 x ^ { 3 } + 27 x + 3 + \frac { 9 x } { x ^ { 2 } - 7 }$ 
B)  $4 x ^ { 3 } + 27 x + 3 - \frac { 9 x } { x ^ { 2 } - 7 }$ 
C)  $4 x ^ { 3 } + 27 x + 3 + \frac { 9 x - 42 } { x ^ { 2 } - 7 }$ 
D)  $4 x ^ { 3 } + 27 x - 3 + \frac { 9 x } { x ^ { 2 } - 7 }$ 
A)  $4 x ^ { 3 } + 27 x + 3 + \frac { 9 x } { x ^ { 2 } - 7 }$ 
B)  $4 x ^ { 3 } + 27 x + 3 - \frac { 9 x } { x ^ { 2 } - 7 }$ 
C)  $4 x ^ { 3 } + 27 x + 3 + \frac { 9 x - 42 } { x ^ { 2 } - 7 }$ 
D)  $4 x ^ { 3 } + 27 x - 3 + \frac { 9 x } { x ^ { 2 } - 7 }$

Question 14

Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval
notation.
-$$( x + 4 ) ( x + 3 ) ( x - 7 ) > 0$$

Accepted Answer

A)  $( - 4 , - 3 ) \cup ( 7 , \infty )$
  
B)  $( - \infty , - 4 ) \cup ( - 3,7 )$
  
C)  $( 7 , \infty )$
  
D)  $( - \infty , - 3 )$
  
A)  $( - 4 , - 3 ) \cup ( 7 , \infty )$
  
B)  $( - \infty , - 4 ) \cup ( - 3,7 )$
  
C)  $( 7 , \infty )$
  
D)  $( - \infty , - 3 )$

Question 15

Find the x-intercepts of the polynomial function. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept.
-$$f ( x ) = - x ^ { 3 } ( x + 4 ) ^ { 2 } ( x - 7 )$$

Accepted Answer

A)  0 , crosses the $x$-axis;
$- 4$, touches the $x$-axis and turns around;
7 , crosses the $x$-axis 
B)  0 , crosses the $x$-axis;
4 , touches the $x$-axis and turns around;
$- 7$, crosses the $x$-axis 
C)  0 , touches the $x$-axis and turns around;
$- 4$, touches the $x$-axis and turns around;
7 , crosses the $x$-axis 
D)  0 , touches the $x$-axis and turns around;
4 , crosses the $x$-axis;
7 , crosses the $x$-axis 
A)  0 , crosses the $x$-axis;
$- 4$, touches the $x$-axis and turns around;
7 , crosses the $x$-axis 
B)  0 , crosses the $x$-axis;
4 , touches the $x$-axis and turns around;
$- 7$, crosses the $x$-axis 
C)  0 , touches the $x$-axis and turns around;
$- 4$, touches the $x$-axis and turns around;
7 , crosses the $x$-axis 
D)  0 , touches the $x$-axis and turns around;
4 , crosses the $x$-axis;
7 , crosses the $x$-axis

Question 16

Graph the polynomial function.
-
f(x)=x3+5x2-x-5

Accepted Answer

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

Question 17

Find the x-intercepts (if any) for the graph of the quadratic function.
-$$y + 4 = ( x + 2 ) ^ { 2 }$$

Accepted Answer

A)  $( 0,0 )$ and $( - 4,0 )$ 
B)  $( 0,0 )$ and $( 4,0 )$ 
C)  $( 4,0 )$ and $( - 4,0 )$ 
D)  $( 0,0 )$ 
A)  $( 0,0 )$ and $( - 4,0 )$ 
B)  $( 0,0 )$ and $( 4,0 )$ 
C)  $( 4,0 )$ and $( - 4,0 )$ 
D)  $( 0,0 )$

Question 18

Solve the problem.
-An arrow is fired into the air with an initial velocity of 128 feet per second. The height in feet of the arrow t seconds after it was shot into the air is given by the function h(x) = -16t2 + 128t. Find the maximum height of the arrow.

Accepted Answer

A)  256 ft 
B)  64 ft 
C)  768 ft 
D)  448 ft 
A)  256 ft 
B)  64 ft 
C)  768 ft 
D)  448 ft

Question 19

Divide using long division.
-$$\left( 11 x ^ { 2 } - 74 x + 48 \right) \div ( x - 6 )$$

Accepted Answer

A)  $11 x - 8$ 
B)  $11 x + 8$ 
C)  $x - 74$ 
D)  $11 \mathrm { x } ^ { 2 } + 74$ 
A)  $11 x - 8$ 
B)  $11 x + 8$ 
C)  $x - 74$ 
D)  $11 \mathrm { x } ^ { 2 } + 74$

Question 20

x Find the range of the quadratic function.
-$$f ( x ) = x ^ { 2 } - 2 x + 9$$

Accepted Answer

A)  $[ 8 , \infty )$ 
B)  $[ - 1 , \infty )$ 
C)  $( - \infty , 8 ]$ 
D)  $( - \infty , 6 ]$ 
A)  $[ 8 , \infty )$ 
B)  $[ - 1 , \infty )$ 
C)  $( - \infty , 8 ]$ 
D)  $( - \infty , 6 ]$

Determine the constant of variation for the stated condition. -f varies jointly as $q ^ { 2 }$ and $h$ , and $f = 64$ when $q = 4$ and $h = 2$ . Find $q$ when $f = 90$ and $h = 5$ .

Find the x-intercepts (if any) for the graph of the quadratic function. - $f ( x ) = x ^ { 2 } - 4$

Determine the constant of variation for the stated condition. - $y = 0.4$ when $x = 0.8$

Determine whether the function is a polynomial function. - $f ( x ) = 10 x ^ { 4 } + 7 x ^ { 3 } + 5$

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

Determine the constant of variation for the stated condition. - $c$ varies directly as $a$ and inversely as $b ; c = 5$ when $a = 65$ and $b = 117$

Determine the maximum possible number of turning points for the graph of the function. - $f ( x ) = - x ^ { 2 } - 6 x + 5$

Find the indicated intercept(s) of the graph of the function. -Is there origin symmetry for the rational function $f ( x ) = \frac { - 4 x } { - 7 x ^ { 2 } + 13 }$ ?

Divide using long division. - $\frac { 10 t ^ { 4 } + 14 t ^ { 3 } - 25 t ^ { 2 } + 39 t - 30 } { 2 t ^ { 2 } + 4 t - 5 }$

Solve the problem. -Solve the equation $8 x ^ { 3 } - 42 x ^ { 2 } + 43 x - 12 = 0$ given that $\frac { 1 } { 2 }$ is a root.

Determine whether the function is a polynomial function. - $f ( x ) = x ^ { 3 / 2 } - x ^ { 5 } + 2$

Divide using long division. - $\left( 4 x ^ { 5 } - x ^ { 3 } + 3 x ^ { 2 } - 180 x - 21 \right) \div \left( x ^ { 2 } - 7 \right)$

Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation. - $( x + 4 ) ( x + 3 ) ( x - 7 ) > 0$

Find the x-intercepts of the polynomial function. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept. - $f ( x ) = - x ^ { 3 } ( x + 4 ) ^ { 2 } ( x - 7 )$

Graph the polynomial function. - f(x)=x³+5x²-x-5

Find the x-intercepts (if any) for the graph of the quadratic function. - $y + 4 = ( x + 2 ) ^ { 2 }$

Solve the problem. -An arrow is fired into the air with an initial velocity of 128 feet per second. The height in feet of the arrow t seconds after it was shot into the air is given by the function h(x) = -16t2 + 128t. Find the maximum height of the arrow.

Divide using long division. - $\left( 11 x ^ { 2 } - 74 x + 48 \right) \div ( x - 6 )$

x Find the range of the quadratic function. - $f ( x ) = x ^ { 2 } - 2 x + 9$

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

Determine the constant of variation for the stated condition. -f varies jointly as q2q ^ { 2 }q2 and hhh , and f=64f = 64f=64 when q=4q = 4q=4 and h=2h = 2h=2 . Find qqq when f=90f = 90f=90 and h=5h = 5h=5 .

Find the x-intercepts (if any) for the graph of the quadratic function. - f(x)=x2−4f ( x ) = x ^ { 2 } - 4f(x)=x2−4

Determine the constant of variation for the stated condition. - y=0.4y = 0.4y=0.4 when x=0.8x = 0.8x=0.8

Determine whether the function is a polynomial function. - f(x)=10x4+7x3+5f ( x ) = 10 x ^ { 4 } + 7 x ^ { 3 } + 5f(x)=10x4+7x3+5

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

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

Determine the constant of variation for the stated condition. - ccc varies directly as aaa and inversely as b;c=5b ; c = 5b;c=5 when a=65a = 65a=65 and b=117b = 117b=117

Determine the maximum possible number of turning points for the graph of the function. - f(x)=−x2−6x+5f ( x ) = - x ^ { 2 } - 6 x + 5f(x)=−x2−6x+5

Find the indicated intercept(s) of the graph of the function. -Is there origin symmetry for the rational function f(x)=−4x−7x2+13f ( x ) = \frac { - 4 x } { - 7 x ^ { 2 } + 13 }f(x)=−7x2+13−4x​ ?

Divide using long division. - 10t4+14t3−25t2+39t−302t2+4t−5\frac { 10 t ^ { 4 } + 14 t ^ { 3 } - 25 t ^ { 2 } + 39 t - 30 } { 2 t ^ { 2 } + 4 t - 5 }2t2+4t−510t4+14t3−25t2+39t−30​

Solve the problem. -Solve the equation 8x3−42x2+43x−12=08 x ^ { 3 } - 42 x ^ { 2 } + 43 x - 12 = 08x3−42x2+43x−12=0 given that 12\frac { 1 } { 2 }21​ is a root.

Determine whether the function is a polynomial function. - f(x)=x3/2−x5+2f ( x ) = x ^ { 3 / 2 } - x ^ { 5 } + 2f(x)=x3/2−x5+2

Divide using long division. - (4x5−x3+3x2−180x−21)÷(x2−7)\left( 4 x ^ { 5 } - x ^ { 3 } + 3 x ^ { 2 } - 180 x - 21 \right) \div \left( x ^ { 2 } - 7 \right)(4x5−x3+3x2−180x−21)÷(x2−7)

Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation. - (x+4)(x+3)(x−7)>0( x + 4 ) ( x + 3 ) ( x - 7 ) > 0(x+4)(x+3)(x−7)>0

Find the x-intercepts of the polynomial function. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept. - f(x)=−x3(x+4)2(x−7)f ( x ) = - x ^ { 3 } ( x + 4 ) ^ { 2 } ( x - 7 )f(x)=−x3(x+4)2(x−7)

Graph the polynomial function. - f(x)=x3+5x2-x-5

Find the x-intercepts (if any) for the graph of the quadratic function. - y+4=(x+2)2y + 4 = ( x + 2 ) ^ { 2 }y+4=(x+2)2