Question 1

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

Accepted Answer

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

Question 2

A quadratic function is given. (a) Express the quadratic function in standard form
b) Find its vertex and its x- and y-intercept(s). $f ( x ) = - 3 x ^ { 2 } + 12 x - 11$

Accepted Answer

(a) @#LAT-DLM& 
b) vertex: @#LAT-DLM& 
,

Question 3

Find the quotient and remainder using long division. $\frac { x ^ { 6 } + x ^ { 2 } + 9 x ^ { 4 } + 9 } { x ^ { 2 } + 9 }$

Accepted Answer

A)  Quotient: $x ^ { 4 } + 1$
; Remainder: $1$ 
B)  Quotient: $x ^ { 2 } + 9$
; Remainder: $0$ 
C)  Quotient: $x ^ { 2 } - 9$
; Remainder: $0$ 
D)  Quotient: $x ^ { 4 } - 1$
; Remainder: $0$ 
E)  none of these 
A)  Quotient: $x ^ { 4 } + 1$
; Remainder: $1$ 
B)  Quotient: $x ^ { 2 } + 9$
; Remainder: $0$ 
C)  Quotient: $x ^ { 2 } - 9$
; Remainder: $0$ 
D)  Quotient: $x ^ { 4 } - 1$
; Remainder: $0$ 
E)  none of these

Question 4

Find the complete factorization of $P ( x ) = x ^ { 4 } - 2 x ^ { 3 } + 2 x ^ { 2 } - 2 x + 1$

Accepted Answer

The answer of Find the complete factorization of \(P (...

Question 5

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)  $\mathrm { HA: } : y = 0$
$\mathrm { V A}$ : $x = - 6$ 
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)  $\mathrm { HA: } : y = 0$
$\mathrm { V A}$ : $x = - 6$ 
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 6

Find all real and complex zeros of $P ( x ) = x ^ { 3 } + x ^ { 2 } - 2$

Accepted Answer

The answer of Find all real and complex zeros of...

Question 7

Sketch the graph of $P$ to find all real zeros. $P ( x ) = x ^ { 4 } - 17 x ^ { 2 } + 16$

Accepted Answer

A)  zeros: $- 2 , - 1,1,2$ 
B)  zeros: $- 4,4 , - 1,1$ 
C)  zeros: $1,4$ 
D)  zeros: $- 4 , - 1,1,0$ 
E)  zeros: $- 1,1,2,16$ 
A)  zeros: $- 2 , - 1,1,2$ 
B)  zeros: $- 4,4 , - 1,1$ 
C)  zeros: $1,4$ 
D)  zeros: $- 4 , - 1,1,0$ 
E)  zeros: $- 1,1,2,16$

Question 8

Graph the rational function. Show clearly all x- and y-intercepts and asymptotes. $y = \frac { x ^ { 3 } + 27 } { x + 5 }$

Accepted Answer

The answer of Graph the rational function. Show clearly all...

Question 9

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

Accepted Answer

A)  $f ( x ) = 2 ( x + 4 ) ^ { 2 } + 9$ 
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)  $f ( x ) = 2 ( x + 4 ) ^ { 2 } + 9$ 
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 10

If a ball is thrown directly upward with a velocity of 48 ft/s, its height (in feet) after t seconds is given
By $y = 48 t - 16 t ^ { 2 }$
) What is the maximum height attained by the ball?

Accepted Answer

A)  $48 \mathrm { ft }$ 
B)  $16 \mathrm { ft }$ 
C)  $32 \mathrm { ft }$ 
D)  $54 \mathrm { ft }$ 
E)  none of these 
A)  $48 \mathrm { ft }$ 
B)  $16 \mathrm { ft }$ 
C)  $32 \mathrm { ft }$ 
D)  $54 \mathrm { ft }$ 
E)  none of these

Question 11

Find a polynomial of degree $4$ , with integer coefficients that has zeros of $3 i$And $2$, with $2$A double zero

Accepted Answer

A)  $x ^ { 4 } + 4 x ^ { 3 } - 5 x ^ { 2 } - 36 x - 36$ 
B)  $x ^ { 4 } + 13 x ^ { 2 } - 4 x ^ { 3 } - 36 x + 36$ 
C)  $x ^ { 4 } + 13 x ^ { 2 } + 4 x ^ { 3 } + 36 x + 36$ 
D)  $4 x ^ { 4 } + x ^ { 3 } - 5 x ^ { 2 } - 36 x - 36$ 
E)  $x ^ { 4 } + 4 x ^ { 3 } + 5 x - 36$ 
A)  $x ^ { 4 } + 4 x ^ { 3 } - 5 x ^ { 2 } - 36 x - 36$ 
B)  $x ^ { 4 } + 13 x ^ { 2 } - 4 x ^ { 3 } - 36 x + 36$ 
C)  $x ^ { 4 } + 13 x ^ { 2 } + 4 x ^ { 3 } + 36 x + 36$ 
D)  $4 x ^ { 4 } + x ^ { 3 } - 5 x ^ { 2 } - 36 x - 36$ 
E)  $x ^ { 4 } + 4 x ^ { 3 } + 5 x - 36$

Question 12

Evaluate the expression and write in the form $a + b i$ . $i ^ { 55 }$

Accepted Answer

A)  $- i$ 
B)  $- 55 i$ 
C)  $- 53 i$ 
D)  $i$ 
E)  $- 1$ 
A)  $- i$ 
B)  $- 55 i$ 
C)  $- 53 i$ 
D)  $i$ 
E)  $- 1$

Question 13

Evaluate the expression and write the result in the form a + bi. $( 3 i ) ^ { 4 }$

Accepted Answer

The answer of Evaluate the expression and write the result...

Question 14

If a ball is thrown directly upward with a velocity of 48 ft/s, its height (in feet) after t seconds is givenby $y = 48 t - 16 t ^ { 2 }$ 
. What is the maximum height attained by the ball?

Accepted Answer

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

Question 15

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

Accepted Answer

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

Question 16

Find the quotient and remainder. $\frac { x ^ { 3 } + 2 x ^ { 2 } - 10 } { x + 3 }$

Accepted Answer

@#LAT-DLM& 
; Quotie

Question 17

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

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 18

Find the equation of the slant asymptote and the vertical asymptote, if any. $r ( x ) = \frac { 2 x ^ { 2 } - 6 x - 7 } { x ^ { 2 } + 4 }$

Accepted Answer

A)  $y = \frac { 1 } { x - 4 } \text {, no vertical asymptote }$ 
B)  $y = 2 x + 2 , x = \pm 2$ 
C)  $x = 2 x + 2 , x = \pm 2$ 
D)  $y = 2 x - 2 , x = \pm 4$ 
E)  $\text { no slant asymptote, no vertical asymptote }$ 
A)  $y = \frac { 1 } { x - 4 } \text {, no vertical asymptote }$ 
B)  $y = 2 x + 2 , x = \pm 2$ 
C)  $x = 2 x + 2 , x = \pm 2$ 
D)  $y = 2 x - 2 , x = \pm 4$ 
E)  $\text { no slant asymptote, no vertical asymptote }$

Question 19

Evaluate the expression $( 1 + i ) ^ { 3 }$ and write in the form $a + b i$

Accepted Answer

A)  $2 j$ 
B)  $1 - 2 i$ 
C)  $1 + 2 i$ 
D)  $- 2 + 2 i$ 
E)  $2 - 2 i$ 
A)  $2 j$ 
B)  $1 - 2 i$ 
C)  $1 + 2 i$ 
D)  $- 2 + 2 i$ 
E)  $2 - 2 i$

Question 20

A manufacturer finds that the revenue generated by selling x units of a certain commodity is given by the function, $R ( x ) = 40 x - 0.2 x ^ { 2 }$ where the revenue $R ( x )$ 
is measured in dollars. What is the maximum revenue, and how many units should be manufactured to obtain this maximum?

Accepted Answer

Maximum Re

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

A quadratic function is given. (a) Express the quadratic function in standard form b) Find its vertex and its x- and y-intercept(s). $f ( x ) = - 3 x ^ { 2 } + 12 x - 11$

Find the quotient and remainder using long division. $\frac { x ^ { 6 } + x ^ { 2 } + 9 x ^ { 4 } + 9 } { x ^ { 2 } + 9 }$

Find the complete factorization of $P ( x ) = x ^ { 4 } - 2 x ^ { 3 } + 2 x ^ { 2 } - 2 x + 1$

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

Find all real and complex zeros of $P ( x ) = x ^ { 3 } + x ^ { 2 } - 2$

Sketch the graph of $P$ to find all real zeros. $P ( x ) = x ^ { 4 } - 17 x ^ { 2 } + 16$

Graph the rational function. Show clearly all x- and y-intercepts and asymptotes. $y = \frac { x ^ { 3 } + 27 } { x + 5 }$

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

If a ball is thrown directly upward with a velocity of 48 ft/s, its height (in feet) after t seconds is given By $y = 48 t - 16 t ^ { 2 }$ ) What is the maximum height attained by the ball?

Find a polynomial of degree $4$ , with integer coefficients that has zeros of $3 i$ And $2$ , with $2$ A double zero

Evaluate the expression and write in the form $a + b i$ . $i ^ { 55 }$

Evaluate the expression and write the result in the form a + bi. $( 3 i ) ^ { 4 }$

If a ball is thrown directly upward with a velocity of 48 ft/s, its height (in feet) after t seconds is givenby $y = 48 t - 16 t ^ { 2 }$ . What is the maximum height attained by the ball?

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

Find the quotient and remainder. $\frac { x ^ { 3 } + 2 x ^ { 2 } - 10 } { x + 3 }$

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

Find the equation of the slant asymptote and the vertical asymptote, if any. $r ( x ) = \frac { 2 x ^ { 2 } - 6 x - 7 } { x ^ { 2 } + 4 }$

Evaluate the expression $( 1 + i ) ^ { 3 }$ and write in the form $a + b i$

A manufacturer finds that the revenue generated by selling x units of a certain commodity is given by the function, $R ( x ) = 40 x - 0.2 x ^ { 2 }$ where the revenue $R ( x )$ is measured in dollars. What is the maximum revenue, and how many units should be manufactured to obtain this maximum?

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

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

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)=−3x2+12x−11f ( x ) = - 3 x ^ { 2 } + 12 x - 11f(x)=−3x2+12x−11

Find the quotient and remainder using long division. x6+x2+9x4+9x2+9\frac { x ^ { 6 } + x ^ { 2 } + 9 x ^ { 4 } + 9 } { x ^ { 2 } + 9 }x2+9x6+x2+9x4+9​

Find the complete factorization of P(x)=x4−2x3+2x2−2x+1P ( x ) = x ^ { 4 } - 2 x ^ { 3 } + 2 x ^ { 2 } - 2 x + 1P(x)=x4−2x3+2x2−2x+1

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

Find all real and complex zeros of P(x)=x3+x2−2P ( x ) = x ^ { 3 } + x ^ { 2 } - 2P(x)=x3+x2−2

Sketch the graph of PPP to find all real zeros. P(x)=x4−17x2+16P ( x ) = x ^ { 4 } - 17 x ^ { 2 } + 16P(x)=x4−17x2+16

Graph the rational function. Show clearly all x- and y-intercepts and asymptotes. y=x3+27x+5y = \frac { x ^ { 3 } + 27 } { x + 5 }y=x+5x3+27​

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

If a ball is thrown directly upward with a velocity of 48 ft/s, its height (in feet) after t seconds is given By y=48t−16t2y = 48 t - 16 t ^ { 2 }y=48t−16t2 ) What is the maximum height attained by the ball?

Find a polynomial of degree 444 , with integer coefficients that has zeros of 3i3 i3i And 222 , with 222 A double zero

Evaluate the expression and write in the form a+bia + b ia+bi . i55i ^ { 55 }i55

Evaluate the expression and write the result in the form a + bi. (3i)4( 3 i ) ^ { 4 }(3i)4

If a ball is thrown directly upward with a velocity of 48 ft/s, its height (in feet) after t seconds is givenby y=48t−16t2y = 48 t - 16 t ^ { 2 }y=48t−16t2 . What is the maximum height attained by the ball?

Find a polynomial of degree 3 that has zeros 1, 2, and -3 and in which the coefficient of xxx is -2.

Find the quotient and remainder. x3+2x2−10x+3\frac { x ^ { 3 } + 2 x ^ { 2 } - 10 } { x + 3 }x+3x3+2x2−10​

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

Find the equation of the slant asymptote and the vertical asymptote, if any. r(x)=2x2−6x−7x2+4r ( x ) = \frac { 2 x ^ { 2 } - 6 x - 7 } { x ^ { 2 } + 4 }r(x)=x2+42x2−6x−7​

Evaluate the expression (1+i)3( 1 + i ) ^ { 3 }(1+i)3 and write in the form a+bia + b ia+bi

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

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

A quadratic function is given. (a) Express the quadratic function in standard form b) Find its vertex and its x- and y-intercept(s). $f ( x ) = - 3 x ^ { 2 } + 12 x - 11$

Find the quotient and remainder using long division. $\frac { x ^ { 6 } + x ^ { 2 } + 9 x ^ { 4 } + 9 } { x ^ { 2 } + 9 }$

Find the complete factorization of $P ( x ) = x ^ { 4 } - 2 x ^ { 3 } + 2 x ^ { 2 } - 2 x + 1$

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

Find all real and complex zeros of $P ( x ) = x ^ { 3 } + x ^ { 2 } - 2$

Sketch the graph of $P$ to find all real zeros. $P ( x ) = x ^ { 4 } - 17 x ^ { 2 } + 16$

Graph the rational function. Show clearly all x- and y-intercepts and asymptotes. $y = \frac { x ^ { 3 } + 27 } { x + 5 }$

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

If a ball is thrown directly upward with a velocity of 48 ft/s, its height (in feet) after t seconds is given By $y = 48 t - 16 t ^ { 2 }$ ) What is the maximum height attained by the ball?

Find a polynomial of degree $4$ , with integer coefficients that has zeros of $3 i$ And $2$ , with $2$ A double zero

Evaluate the expression and write in the form $a + b i$ . $i ^ { 55 }$

Evaluate the expression and write the result in the form a + bi. $( 3 i ) ^ { 4 }$

If a ball is thrown directly upward with a velocity of 48 ft/s, its height (in feet) after t seconds is givenby $y = 48 t - 16 t ^ { 2 }$ . What is the maximum height attained by the ball?

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

Find the quotient and remainder. $\frac { x ^ { 3 } + 2 x ^ { 2 } - 10 } { x + 3 }$

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

Find the equation of the slant asymptote and the vertical asymptote, if any. $r ( x ) = \frac { 2 x ^ { 2 } - 6 x - 7 } { x ^ { 2 } + 4 }$

Evaluate the expression $( 1 + i ) ^ { 3 }$ and write in the form $a + b i$