Question 1

Find the y-intercept of the polynomial function.
-$$f ( x ) = 5 - x ^ { 4 }$$

Accepted Answer

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

Question 2

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. Then use this end
-$$f ( x ) = x ^ { 3 } - 4 x ^ { 2 } + 3 x - 2$$

Accepted Answer

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

Question 3

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.
-$$f ( x ) = x ^ { 4 } - 25 x ^ { 2 }$$

Accepted Answer

A)  0 , touches the $x$-axis and turns around;
5 , crosses the $x$-axis;
$- 5$, crosses the $x$-axis 
B)  0 , crosses the $x$-axis;
5 , crosses the $x$-axis;
$- 5$, crosses the $x$-axis 
C)  0 , touches the $x$-axis and turns around
25 , touches the $x$-axis and turns around 
D)  0 , touches the $x$-axis and turns around;
25 , crosses the $x$-axis 
A)  0 , touches the $x$-axis and turns around;
5 , crosses the $x$-axis;
$- 5$, crosses the $x$-axis 
B)  0 , crosses the $x$-axis;
5 , crosses the $x$-axis;
$- 5$, crosses the $x$-axis 
C)  0 , touches the $x$-axis and turns around
25 , touches the $x$-axis and turns around 
D)  0 , touches the $x$-axis and turns around;
25 , crosses the $x$-axis

Question 4

Use the Intermediate Value Theorem to determine whether the polynomial function has a real zero between the
given integers.
-$f ( x ) = - 6 x ^ { 4 } - 10 x ^ { 2 } + 2$; between $- 1$ and 0

Accepted Answer

A)  $f ( - 1 ) = - 14$ and $f ( 0 ) = 2$; yes 
B)  $f ( - 1 ) = 14$ and $f ( 0 ) = 3$; no 
C)  $\mathrm { f } ( - 1 ) = - 14$ and $\mathrm { f } ( 0 ) = - 2$; no 
D)  $f ( - 1 ) = 14$ and $f ( 0 ) = - 2$; yes 
A)  $f ( - 1 ) = - 14$ and $f ( 0 ) = 2$; yes 
B)  $f ( - 1 ) = 14$ and $f ( 0 ) = 3$; no 
C)  $\mathrm { f } ( - 1 ) = - 14$ and $\mathrm { f } ( 0 ) = - 2$; no 
D)  $f ( - 1 ) = 14$ and $f ( 0 ) = - 2$; yes

Question 5

Solve the problem.
-The sum of 81 times a number and the reciprocal of the number is positive. Find the numbers which satisfy this condition.

Accepted Answer

A)  any number greater than 0 
B)  any number greater than $\frac { 1 } { 9 }$ 
C)  any number between $- \frac { 1 } { 9 }$ and $\frac { 1 } { 9 }$ 
D)  any number between 0 and $\frac { 1 } { 9 }$ 
A)  any number greater than 0 
B)  any number greater than $\frac { 1 } { 9 }$ 
C)  any number between $- \frac { 1 } { 9 }$ and $\frac { 1 } { 9 }$ 
D)  any number between 0 and $\frac { 1 } { 9 }$

Question 6

Find the slant asymptote, if any, of the graph of the rational function.
-$$f ( x ) = \frac { 9 x ^ { 2 } } { 7 x ^ { 2 } + 5 }$$

Accepted Answer

A)  $y = 9 x$ 
B)  $y = x + 9$ 
C)  $y = x + \frac { 9 } { 7 }$ 
D)  no slant asymptote 
A)  $y = 9 x$ 
B)  $y = x + 9$ 
C)  $y = x + \frac { 9 } { 7 }$ 
D)  no slant asymptote

Question 7

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

Accepted Answer

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

Question 8

x Find the range of the quadratic function.
-$$f ( x ) = ( x + 5 ) ^ { 2 } - 3$$

Accepted Answer

A)  $[ - 3 , \infty )$ 
B)  $( - \infty , - 5 ]$ 
C)  $( - \infty , - 3 ]$ 
D)  $[ - 5 , \infty )$ 
A)  $[ - 3 , \infty )$ 
B)  $( - \infty , - 5 ]$ 
C)  $( - \infty , - 3 ]$ 
D)  $[ - 5 , \infty )$

Question 9

Determine whether the function is a polynomial function.
-$$h ( x ) = 16 x + 4$$

Accepted Answer

A)  1 
B)  2 
C)  0 
D)  16 
A)  1 
B)  2 
C)  0 
D)  16

Question 10

Find the zeros of the polynomial function.
-$$f ( x ) = x ^ { 3 } + x ^ { 2 } - 42 x$$

Accepted Answer

A)  $x = 0 , x = - 7 , x = 6$ 
B)  $x = - 7 , x = 6$ 
C)  $x = 5 , x = 6$ 
D)  $x = 0 , x = 5 , x = 6$ x 
A)  $x = 0 , x = - 7 , x = 6$ 
B)  $x = - 7 , x = 6$ 
C)  $x = 5 , x = 6$ 
D)  $x = 0 , x = 5 , x = 6$ x

Question 11

Solve the problem.
-A ball is thrown vertically upward with an initial velocity of 128 feet per second. The distance in feet of the ball from the ground after $t$ seconds is $s = 128 t - 16 t ^ { 2 }$. For what intervals of time is the ball less than 240 above the ground (after it is tossed until it returns to the ground)?

Accepted Answer

A)  between 0 and 3 seconds and between 5 and 8 seconds 
B)  between 3 and 5 seconds 
C)  between 0 and $2.5$ seconds and between $5.5$ and 8 seconds 
D)  between 0 and $3.5$ seconds and between $4.5$ and 8 seconds 
A)  between 0 and 3 seconds and between 5 and 8 seconds 
B)  between 3 and 5 seconds 
C)  between 0 and $2.5$ seconds and between $5.5$ and 8 seconds 
D)  between 0 and $3.5$ seconds and between $4.5$ and 8 seconds

Question 12

Divide using synthetic division.
-$\frac { - 4 x ^ { 3 } - 8 x ^ { 2 } + 18 x + 18 } { x + 3 }$

Accepted Answer

A)  $- 4 x ^ { 2 } + 4 x + 6$ 
B)  $4 x ^ { 2 } - 3 x + 6$ 
C) $ - \frac { 4 } { 3 } x ^ { 2 } - \frac { 8 } { 3 } x + 6$ 
D)  $- 4 x ^ { 2 } x - \frac { 8 } { 3 } + 6$ 
A)  $- 4 x ^ { 2 } + 4 x + 6$ 
B)  $4 x ^ { 2 } - 3 x + 6$ 
C) $ - \frac { 4 } { 3 } x ^ { 2 } - \frac { 8 } { 3 } x + 6$ 
D)  $- 4 x ^ { 2 } x - \frac { 8 } { 3 } + 6$

Question 13

Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval
notation.
-$$x ^ { 2 } - 14 x + 49 > 0$$

Accepted Answer

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

Question 14

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.
-$$f ( x ) = 9 - ( x - 3 ) ^ { 2 }$$

Accepted Answer

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

Question 15

Determine the maximum possible number of turning points for the graph of the function.
-Suppose that a polynomial function is used to model the data shown in the graph below.  
For what intervals is the function increasing?

Accepted Answer

A)  0 through 10 and 30 through 50 
B)  0 through 50 
C)  0 through 20 and 30 through 50 
D)  0 through 10 and 40 through 50 
A)  0 through 10 and 30 through 50 
B)  0 through 50 
C)  0 through 20 and 30 through 50 
D)  0 through 10 and 40 through 50

Question 16

Solve Problems Involving Joint Variation
-$p$ varies jointly as the square of $q$ and the square of $r$.

Accepted Answer

A)  $p = k q ^ { 2 } r ^ { 2 }$ 
B)  $\mathrm { pq } ^ { 2 } \mathrm { r } ^ { 2 } = \mathrm { k }$ 
C)  $\mathrm { p } = \mathrm { k } + \mathrm { q } ^ { 2 } + \mathrm { r } ^ { 2 }$ 
D)  $p + q ^ { 2 } + r ^ { 2 } = k$ 
A)  $p = k q ^ { 2 } r ^ { 2 }$ 
B)  $\mathrm { pq } ^ { 2 } \mathrm { r } ^ { 2 } = \mathrm { k }$ 
C)  $\mathrm { p } = \mathrm { k } + \mathrm { q } ^ { 2 } + \mathrm { r } ^ { 2 }$ 
D)  $p + q ^ { 2 } + r ^ { 2 } = k$

Question 17

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

Accepted Answer

A)  $x = - 3 , x = 3$, 
B)  $x = 3 , x = 4$ 
C)  $x = - 3 , x = 4$ 
D)  $x = 3 , x = - 3 , x = 4$ 
A)  $x = - 3 , x = 3$, 
B)  $x = 3 , x = 4$ 
C)  $x = - 3 , x = 4$ 
D)  $x = 3 , x = - 3 , x = 4$

Question 18

Find the x-intercepts (if any) for the graph of the quadratic function.
-$$f ( x ) = 2 x ^ { 2 } - 6 x - 20$$

Accepted Answer

A)  $( - 2,0 )$ and $( 5,0 )$ 
B)  $( 2,0 )$ and $( - 5,0 )$ 
C)  $( - 2,0 )$ and $( - 5,0 )$ 
D)  $( 2,0 )$ and $( 5,0 )$ 
A)  $( - 2,0 )$ and $( 5,0 )$ 
B)  $( 2,0 )$ and $( - 5,0 )$ 
C)  $( - 2,0 )$ and $( - 5,0 )$ 
D)  $( 2,0 )$ and $( 5,0 )$

Question 19

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

Accepted Answer

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

Question 20

Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses
the x-axis or touches the x-axis and turns around, at each zero.
-$$f ( x ) = x ^ { 3 } + 9 x ^ { 2 } + 24 x + 20$$

Accepted Answer

A)  $- 2$, multiplicity 2, touches the $x$-axis and turns around;
 $- 5$, multiplicity 1 , crosses the $x$-axis. 
B)  $- 2$, multiplicity 2 , crosses the x-axis;
 $- 5$, multiplicity 1 , touches the $x$-axis and turns around 
C)  2, multiplicity 1, crosses the x-axis;
$- 2$, multiplicity 1 , crosses the $x$-axis;
$- 5$, multiplicity 1 , crosses the $x$-axis. 
D)  2, multiplicity 1, crosses the x-axis;
$- 2$, multiplicity 2 , touches the $x$-axis and turns around;
$- 5$, multiplicity 1 , crosses the $x$-axis. 
A)  $- 2$, multiplicity 2, touches the $x$-axis and turns around;
 $- 5$, multiplicity 1 , crosses the $x$-axis. 
B)  $- 2$, multiplicity 2 , crosses the x-axis;
 $- 5$, multiplicity 1 , touches the $x$-axis and turns around 
C)  2, multiplicity 1, crosses the x-axis;
$- 2$, multiplicity 1 , crosses the $x$-axis;
$- 5$, multiplicity 1 , crosses the $x$-axis. 
D)  2, multiplicity 1, crosses the x-axis;
$- 2$, multiplicity 2 , touches the $x$-axis and turns around;
$- 5$, multiplicity 1 , crosses the $x$-axis.

Find the y-intercept of the polynomial function. - $f ( x ) = 5 - x ^ { 4 }$

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. Then use this end - $f ( x ) = x ^ { 3 } - 4 x ^ { 2 } + 3 x - 2$

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. - $f ( x ) = x ^ { 4 } - 25 x ^ { 2 }$

Use the Intermediate Value Theorem to determine whether the polynomial function has a real zero between the given integers. - $f ( x ) = - 6 x ^ { 4 } - 10 x ^ { 2 } + 2$ ; between $- 1$ and 0

Solve the problem. -The sum of 81 times a number and the reciprocal of the number is positive. Find the numbers which satisfy this condition.

Find the slant asymptote, if any, of the graph of the rational function. - $f ( x ) = \frac { 9 x ^ { 2 } } { 7 x ^ { 2 } + 5 }$

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

x Find the range of the quadratic function. - $f ( x ) = ( x + 5 ) ^ { 2 } - 3$

Determine whether the function is a polynomial function. - $h ( x ) = 16 x + 4$

Find the zeros of the polynomial function. - $f ( x ) = x ^ { 3 } + x ^ { 2 } - 42 x$

Divide using synthetic division. - $\frac { - 4 x ^ { 3 } - 8 x ^ { 2 } + 18 x + 18 } { x + 3 }$

Determine the maximum possible number of turning points for the graph of the function. -Suppose that a polynomial function is used to model the data shown in the graph below. For what intervals is the function increasing?

Solve Problems Involving Joint Variation - $p$ varies jointly as the square of $q$ and the square of $r$ .

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

Find the x-intercepts (if any) for the graph of the quadratic function. - $f ( x ) = 2 x ^ { 2 } - 6 x - 20$

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

Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis or touches the x-axis and turns around, at each zero. - $f ( x ) = x ^ { 3 } + 9 x ^ { 2 } + 24 x + 20$

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 y-intercept of the polynomial function. - f(x)=5−x4f ( x ) = 5 - x ^ { 4 }f(x)=5−x4

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. Then use this end - f(x)=x3−4x2+3x−2f ( x ) = x ^ { 3 } - 4 x ^ { 2 } + 3 x - 2f(x)=x3−4x2+3x−2

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)=x4−25x2f ( x ) = x ^ { 4 } - 25 x ^ { 2 }f(x)=x4−25x2

Use the Intermediate Value Theorem to determine whether the polynomial function has a real zero between the given integers. - f(x)=−6x4−10x2+2f ( x ) = - 6 x ^ { 4 } - 10 x ^ { 2 } + 2f(x)=−6x4−10x2+2 ; between −1- 1−1 and 0

Solve the problem. -The sum of 81 times a number and the reciprocal of the number is positive. Find the numbers which satisfy this condition.

Find the slant asymptote, if any, of the graph of the rational function. - f(x)=9x27x2+5f ( x ) = \frac { 9 x ^ { 2 } } { 7 x ^ { 2 } + 5 }f(x)=7x2+59x2​

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

x Find the range of the quadratic function. - f(x)=(x+5)2−3f ( x ) = ( x + 5 ) ^ { 2 } - 3f(x)=(x+5)2−3

Determine whether the function is a polynomial function. - h(x)=16x+4h ( x ) = 16 x + 4h(x)=16x+4

Find the zeros of the polynomial function. - f(x)=x3+x2−42xf ( x ) = x ^ { 3 } + x ^ { 2 } - 42 xf(x)=x3+x2−42x

Divide using synthetic division. - −4x3−8x2+18x+18x+3\frac { - 4 x ^ { 3 } - 8 x ^ { 2 } + 18 x + 18 } { x + 3 }x+3−4x3−8x2+18x+18​

Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation. - x2−14x+49>0x ^ { 2 } - 14 x + 49 > 0x2−14x+49>0

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)=9−(x−3)2f ( x ) = 9 - ( x - 3 ) ^ { 2 }f(x)=9−(x−3)2

Determine the maximum possible number of turning points for the graph of the function. -Suppose that a polynomial function is used to model the data shown in the graph below. For what intervals is the function increasing?

Solve Problems Involving Joint Variation - ppp varies jointly as the square of qqq and the square of rrr .

Find the zeros of the polynomial function. - f(x)=3(x+3)(x−3)4f ( x ) = 3 ( x + 3 ) ( x - 3 ) ^ { 4 }f(x)=3(x+3)(x−3)4

Find the x-intercepts (if any) for the graph of the quadratic function. - f(x)=2x2−6x−20f ( x ) = 2 x ^ { 2 } - 6 x - 20f(x)=2x2−6x−20

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

Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis or touches the x-axis and turns around, at each zero. - f(x)=x3+9x2+24x+20f ( x ) = x ^ { 3 } + 9 x ^ { 2 } + 24 x + 20f(x)=x3+9x2+24x+20

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 y-intercept of the polynomial function. - $f ( x ) = 5 - x ^ { 4 }$

Use the Leading Coefficient Test to determine the end behavior of the polynomial function. Then use this end - $f ( x ) = x ^ { 3 } - 4 x ^ { 2 } + 3 x - 2$

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. - $f ( x ) = x ^ { 4 } - 25 x ^ { 2 }$

Use the Intermediate Value Theorem to determine whether the polynomial function has a real zero between the given integers. - $f ( x ) = - 6 x ^ { 4 } - 10 x ^ { 2 } + 2$ ; between $- 1$ and 0

Find the slant asymptote, if any, of the graph of the rational function. - $f ( x ) = \frac { 9 x ^ { 2 } } { 7 x ^ { 2 } + 5 }$

x Find the range of the quadratic function. - $f ( x ) = ( x + 5 ) ^ { 2 } - 3$

Determine whether the function is a polynomial function. - $h ( x ) = 16 x + 4$

Find the zeros of the polynomial function. - $f ( x ) = x ^ { 3 } + x ^ { 2 } - 42 x$

Divide using synthetic division. - $\frac { - 4 x ^ { 3 } - 8 x ^ { 2 } + 18 x + 18 } { x + 3 }$

Solve Problems Involving Joint Variation - $p$ varies jointly as the square of $q$ and the square of $r$ .

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

Find the x-intercepts (if any) for the graph of the quadratic function. - $f ( x ) = 2 x ^ { 2 } - 6 x - 20$

Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis or touches the x-axis and turns around, at each zero. - $f ( x ) = x ^ { 3 } + 9 x ^ { 2 } + 24 x + 20$