Question 1

Sketch the graph of the function $P ( x ) = ( x - 1 ) ^ { 4 } + 16$ by transforming the graph of an appropriate function of the form $y = x ^ { n }$

Accepted Answer

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

Question 2

Find all rational, irrational, and complex zeros. $P ( x ) = x ^ { 4 } + x ^ { 3 } - 5 x ^ { 2 } - 3 x + 6$

Accepted Answer

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

Question 3

Sketch the graph of the function $y = ( x - 3 ) ^ { 2 }$  by transforming the graph of an appropriate function of the form $y = x ^ { n }$  . Indicate all $x$  - and $y -$  intercepts on your graph.

Accepted Answer

The answer of Sketch the graph of the function \(y...

Question 4

Graph the rational function. $y = \frac { 2 x + 4 } { x - 2 }$

Accepted Answer

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

Question 5

Graph the rational function. $y = \frac { 2 x + 4 } { x - 2 }$

Accepted Answer

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

Question 6

Find all rational, irrational, and complex zeros (and state their multiplicities). $P ( x ) = x ^ { 4 } + 10 x ^ { 2 } - 2 x ^ { 3 } - 18 x + 9$

Accepted Answer

The answer of Find all rational, irrational, and complex zeros...

Question 7

Determine the number of possible positive and negative real zeros using Descartes' Rule of Signs. $p ( x ) = x ^ { 5 } - 4 x ^ { 4 } - 13 x ^ { 3 } + 70 x ^ { 2 } - 90 x + 36$

Accepted Answer

A)  Positive real: exactly one; Negative real: exactly one 
B)  Positive real: 2 or 0; Negative real: exactly 2 
C)  Positive real: 4 or 0; Negative real: exactly one 
D)  Positive real: exactly 4; Negative real: exactly one 
E)  Positive real: 4, 2, or 0; Negative real: exactly one 
A)  Positive real: exactly one; Negative real: exactly one 
B)  Positive real: 2 or 0; Negative real: exactly 2 
C)  Positive real: 4 or 0; Negative real: exactly one 
D)  Positive real: exactly 4; Negative real: exactly one 
E)  Positive real: 4, 2, or 0; Negative real: exactly one

Question 8

If a ball is thrown directly upward with a velocity of 64 ft/s, its height (in feet) after t seconds is given
by $y = 64 t - 16 t ^ { 2 }$ 
. What is the maximum height attained by the ball?

Accepted Answer

The answer of If a ball is thrown directly upward...

Question 9

Find the quotient and remainder. $\frac { x ^ { 3 } + 3 x - 2 } { x - 1 }$

Accepted Answer

quotient @#LAT-DLM&

Question 10

Find the indicated value of the polynomial using the Remainder Theorem. $p ( x ) = x ^ { 3 } - 2 x ^ { 2 } - 76$ 
; find $p ( - 4 )$

Accepted Answer

The answer of Find the indicated value of the polynomial...

Question 11

Find a polynomial of degree 3 that has zeros 1, 2, and -5 and in which the coefficient of $x ^ { 2 }$ is 3.

Accepted Answer

The answer of Find a polynomial of degree 3 that...

Question 12

Find all rational, irrational, and complex zeros. $P ( x ) = x ^ { 4 } - 81$

Accepted Answer

A)  $\{ - 3,3 , - 3 i , 3 i \}$ 
B)  $\{ - 3,3 \}$ 
C)  $\{ 3 \}$ 
D)  $( - 3 i , 3 i \}$ 
E)  $\{ - 9,9 , - 3 i , 3 i \}$ 
A)  $\{ - 3,3 , - 3 i , 3 i \}$ 
B)  $\{ - 3,3 \}$ 
C)  $\{ 3 \}$ 
D)  $( - 3 i , 3 i \}$ 
E)  $\{ - 9,9 , - 3 i , 3 i \}$

Question 13

Find all rational, irrational, and complex zeros (and state their multiplicities). $P ( x ) = x ^ { 3 } - 8$

Accepted Answer

The answer of Find all rational, irrational, and complex zeros...

Question 14

Graph the rational function. $y = \frac { 2 x + 4 } { x - 2 }$

Accepted Answer

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

Question 15

Find all horizontal and vertical asymptotes of the function $y ( x ) = \frac { 6 } { x - 6 }$ .

Accepted Answer

A)  HA: $x - a x i s$
$\mathrm { VA } : x = 6$ 
B)  $\mathrm { HA: } : y = 0$
$\mathrm { VA}$ : $x = - 6$ 
C)  $\mathrm { HA }$ : none
$\mathrm { VA } : x = 6$ 
D)  $\mathrm { HA }$ : none
$\mathrm { VA } : x = 1$ 
E)  $\mathrm { HA } : y = 6$
$\mathrm { VA } : x = 6$ 
A)  HA: $x - a x i s$
$\mathrm { VA } : x = 6$ 
B)  $\mathrm { HA: } : y = 0$
$\mathrm { VA}$ : $x = - 6$ 
C)  $\mathrm { HA }$ : none
$\mathrm { VA } : x = 6$ 
D)  $\mathrm { HA }$ : none
$\mathrm { VA } : x = 1$ 
E)  $\mathrm { HA } : y = 6$
$\mathrm { VA } : x = 6$

Question 16

Divide. $\frac { x ^ { 3 } + 2 x ^ { 2 } - 10 } { x + 3 }$

Accepted Answer

The answer of Divide. \(\frac { x ^ { 3...

Question 17

Express the quadratic function in standard form. $f ( x ) = 2 x ^ { 2 } + 8 x + 9$

Accepted Answer

A)  $f ( x ) = 2 ( x + 2 ) ^ { 2 } + 9$ 
B)  $f ( x ) = ( x + 2 ) ^ { 2 } + 2$ 
C)  $f ( x ) = 2 ( x + 1 ) ^ { 2 } + 1$ 
D)  $f ( x ) = 2 ( x + 1 ) ^ { 2 } + 2$ 
E)  none of these 
A)  $f ( x ) = 2 ( x + 2 ) ^ { 2 } + 9$ 
B)  $f ( x ) = ( x + 2 ) ^ { 2 } + 2$ 
C)  $f ( x ) = 2 ( x + 1 ) ^ { 2 } + 1$ 
D)  $f ( x ) = 2 ( x + 1 ) ^ { 2 } + 2$ 
E)  none of these

Question 18

A quadratic function is given. 
(a) Express the quadratic function in standard form
b) Find its vertex and its x- and y-intercept(s). $f ( x ) = 2 x ^ { 2 } + 8 x + 9$

Accepted Answer

@#LAT-DLM& 
b) verte

Question 19

Find the quotient and remainder. $\frac { x ^ { 4 } - 2 x ^ { 2 } + 7 x } { x ^ { 2 } - x + 3 }$

Accepted Answer

Quotient:

Question 20

List all possible rational roots. $x ^ { 5 } - 4 x ^ { 4 } - 13 x ^ { 3 } + 70 x ^ { 2 } - 90 x + 36$

Accepted Answer

@#LAT-DLM& , @#LAT-DLM& , @#LAT-DLM& , @#LAT-DLM&

Sketch the graph of the function $P ( x ) = ( x - 1 ) ^ { 4 } + 16$ by transforming the graph of an appropriate function of the form $y = x ^ { n }$

Find all rational, irrational, and complex zeros. $P ( x ) = x ^ { 4 } + x ^ { 3 } - 5 x ^ { 2 } - 3 x + 6$

Sketch the graph of the function $y = ( x - 3 ) ^ { 2 }$ by transforming the graph of an appropriate function of the form $y = x ^ { n }$ . Indicate all $x$ - and $y -$ intercepts on your graph.

Graph the rational function. $y = \frac { 2 x + 4 } { x - 2 }$

Graph the rational function. $y = \frac { 2 x + 4 } { x - 2 }$

Find all rational, irrational, and complex zeros (and state their multiplicities). $P ( x ) = x ^ { 4 } + 10 x ^ { 2 } - 2 x ^ { 3 } - 18 x + 9$

Determine the number of possible positive and negative real zeros using Descartes' Rule of Signs. $p ( x ) = x ^ { 5 } - 4 x ^ { 4 } - 13 x ^ { 3 } + 70 x ^ { 2 } - 90 x + 36$

If a ball is thrown directly upward with a velocity of 64 ft/s, its height (in feet) after t seconds is given by $y = 64 t - 16 t ^ { 2 }$ . What is the maximum height attained by the ball?

Find the quotient and remainder. $\frac { x ^ { 3 } + 3 x - 2 } { x - 1 }$

Find the indicated value of the polynomial using the Remainder Theorem. $p ( x ) = x ^ { 3 } - 2 x ^ { 2 } - 76$ ; find $p ( - 4 )$

Find a polynomial of degree 3 that has zeros 1, 2, and -5 and in which the coefficient of $x ^ { 2 }$ is 3.

Find all rational, irrational, and complex zeros. $P ( x ) = x ^ { 4 } - 81$

Find all rational, irrational, and complex zeros (and state their multiplicities). $P ( x ) = x ^ { 3 } - 8$

Graph the rational function. $y = \frac { 2 x + 4 } { x - 2 }$

Find all horizontal and vertical asymptotes of the function $y ( x ) = \frac { 6 } { x - 6 }$ .

Divide. $\frac { x ^ { 3 } + 2 x ^ { 2 } - 10 } { x + 3 }$

Express the quadratic function in standard form. $f ( x ) = 2 x ^ { 2 } + 8 x + 9$

A quadratic function is given. (a) Express the quadratic function in standard form b) Find its vertex and its x- and y-intercept(s). $f ( x ) = 2 x ^ { 2 } + 8 x + 9$

Find the quotient and remainder. $\frac { x ^ { 4 } - 2 x ^ { 2 } + 7 x } { x ^ { 2 } - x + 3 }$

List all possible rational roots. $x ^ { 5 } - 4 x ^ { 4 } - 13 x ^ { 3 } + 70 x ^ { 2 } - 90 x + 36$

Equations and Graphs

Functions

Polynomial and Rational Functions

Trigonometric Functions: Right Triangle Approach

Trigonometric Functions: Unit Circle Approach

Conic Sections

Polar Coordinates and Parametric Equations

Vectors in Two and Three Dimensions

Systems of Equations and Inequalities

Matrices and Determinants

Conic Sections

Sequences and Series

Counting and Probability

Filters

Exam 4: Exponential and Logarithmic Functions

Sketch the graph of the function P(x)=(x−1)4+16P ( x ) = ( x - 1 ) ^ { 4 } + 16P(x)=(x−1)4+16 by transforming the graph of an appropriate function of the form y=xny = x ^ { n }y=xn

Find all rational, irrational, and complex zeros. P(x)=x4+x3−5x2−3x+6P ( x ) = x ^ { 4 } + x ^ { 3 } - 5 x ^ { 2 } - 3 x + 6P(x)=x4+x3−5x2−3x+6

Sketch the graph of the function y=(x−3)2y = ( x - 3 ) ^ { 2 }y=(x−3)2 by transforming the graph of an appropriate function of the form y=xny = x ^ { n }y=xn . Indicate all xxx - and y−y -y− intercepts on your graph.

Graph the rational function. y=2x+4x−2y = \frac { 2 x + 4 } { x - 2 }y=x−22x+4​

Graph the rational function. y=2x+4x−2y = \frac { 2 x + 4 } { x - 2 }y=x−22x+4​

Find all rational, irrational, and complex zeros (and state their multiplicities). P(x)=x4+10x2−2x3−18x+9P ( x ) = x ^ { 4 } + 10 x ^ { 2 } - 2 x ^ { 3 } - 18 x + 9P(x)=x4+10x2−2x3−18x+9

Determine the number of possible positive and negative real zeros using Descartes' Rule of Signs. p(x)=x5−4x4−13x3+70x2−90x+36p ( x ) = x ^ { 5 } - 4 x ^ { 4 } - 13 x ^ { 3 } + 70 x ^ { 2 } - 90 x + 36p(x)=x5−4x4−13x3+70x2−90x+36

If a ball is thrown directly upward with a velocity of 64 ft/s, its height (in feet) after t seconds is given by y=64t−16t2y = 64 t - 16 t ^ { 2 }y=64t−16t2 . What is the maximum height attained by the ball?

Find the quotient and remainder. x3+3x−2x−1\frac { x ^ { 3 } + 3 x - 2 } { x - 1 }x−1x3+3x−2​

Find the indicated value of the polynomial using the Remainder Theorem. p(x)=x3−2x2−76p ( x ) = x ^ { 3 } - 2 x ^ { 2 } - 76p(x)=x3−2x2−76 ; find p(−4)p ( - 4 )p(−4)

Find a polynomial of degree 3 that has zeros 1, 2, and -5 and in which the coefficient of x2x ^ { 2 }x2 is 3.

Find all rational, irrational, and complex zeros. P(x)=x4−81P ( x ) = x ^ { 4 } - 81P(x)=x4−81

Find all rational, irrational, and complex zeros (and state their multiplicities). P(x)=x3−8P ( x ) = x ^ { 3 } - 8P(x)=x3−8

Graph the rational function. y=2x+4x−2y = \frac { 2 x + 4 } { x - 2 }y=x−22x+4​

Find all horizontal and vertical asymptotes of the function y(x)=6x−6y ( x ) = \frac { 6 } { x - 6 }y(x)=x−66​ .

Divide. x3+2x2−10x+3\frac { x ^ { 3 } + 2 x ^ { 2 } - 10 } { x + 3 }x+3x3+2x2−10​

Express the quadratic function in standard form. f(x)=2x2+8x+9f ( x ) = 2 x ^ { 2 } + 8 x + 9f(x)=2x2+8x+9

A quadratic function is given. (a) Express the quadratic function in standard form b) Find its vertex and its x- and y-intercept(s). f(x)=2x2+8x+9f ( x ) = 2 x ^ { 2 } + 8 x + 9f(x)=2x2+8x+9

Find the quotient and remainder. x4−2x2+7xx2−x+3\frac { x ^ { 4 } - 2 x ^ { 2 } + 7 x } { x ^ { 2 } - x + 3 }x2−x+3x4−2x2+7x​

List all possible rational roots. x5−4x4−13x3+70x2−90x+36x ^ { 5 } - 4 x ^ { 4 } - 13 x ^ { 3 } + 70 x ^ { 2 } - 90 x + 36x5−4x4−13x3+70x2−90x+36

Equations and Graphs

Functions

Polynomial and Rational Functions

Trigonometric Functions: Right Triangle Approach

Trigonometric Functions: Unit Circle Approach

Conic Sections

Polar Coordinates and Parametric Equations

Vectors in Two and Three Dimensions

Systems of Equations and Inequalities

Matrices and Determinants

Conic Sections

Sequences and Series

Counting and Probability

Filters

Sketch the graph of the function $P ( x ) = ( x - 1 ) ^ { 4 } + 16$ by transforming the graph of an appropriate function of the form $y = x ^ { n }$

Find all rational, irrational, and complex zeros. $P ( x ) = x ^ { 4 } + x ^ { 3 } - 5 x ^ { 2 } - 3 x + 6$

Sketch the graph of the function $y = ( x - 3 ) ^ { 2 }$ by transforming the graph of an appropriate function of the form $y = x ^ { n }$ . Indicate all $x$ - and $y -$ intercepts on your graph.

Graph the rational function. $y = \frac { 2 x + 4 } { x - 2 }$

Graph the rational function. $y = \frac { 2 x + 4 } { x - 2 }$

Find all rational, irrational, and complex zeros (and state their multiplicities). $P ( x ) = x ^ { 4 } + 10 x ^ { 2 } - 2 x ^ { 3 } - 18 x + 9$

Determine the number of possible positive and negative real zeros using Descartes' Rule of Signs. $p ( x ) = x ^ { 5 } - 4 x ^ { 4 } - 13 x ^ { 3 } + 70 x ^ { 2 } - 90 x + 36$

If a ball is thrown directly upward with a velocity of 64 ft/s, its height (in feet) after t seconds is given by $y = 64 t - 16 t ^ { 2 }$ . What is the maximum height attained by the ball?

Find the quotient and remainder. $\frac { x ^ { 3 } + 3 x - 2 } { x - 1 }$

Find the indicated value of the polynomial using the Remainder Theorem. $p ( x ) = x ^ { 3 } - 2 x ^ { 2 } - 76$ ; find $p ( - 4 )$

Find a polynomial of degree 3 that has zeros 1, 2, and -5 and in which the coefficient of $x ^ { 2 }$ is 3.

Find all rational, irrational, and complex zeros. $P ( x ) = x ^ { 4 } - 81$

Find all rational, irrational, and complex zeros (and state their multiplicities). $P ( x ) = x ^ { 3 } - 8$

Graph the rational function. $y = \frac { 2 x + 4 } { x - 2 }$

Find all horizontal and vertical asymptotes of the function $y ( x ) = \frac { 6 } { x - 6 }$ .

Divide. $\frac { x ^ { 3 } + 2 x ^ { 2 } - 10 } { x + 3 }$

Express the quadratic function in standard form. $f ( x ) = 2 x ^ { 2 } + 8 x + 9$

A quadratic function is given. (a) Express the quadratic function in standard form b) Find its vertex and its x- and y-intercept(s). $f ( x ) = 2 x ^ { 2 } + 8 x + 9$

Find the quotient and remainder. $\frac { x ^ { 4 } - 2 x ^ { 2 } + 7 x } { x ^ { 2 } - x + 3 }$

List all possible rational roots. $x ^ { 5 } - 4 x ^ { 4 } - 13 x ^ { 3 } + 70 x ^ { 2 } - 90 x + 36$