Question 1

Select from the following which is the polynomial function that has the given zeros.   $5 , - 7$

Accepted Answer

A)  $f ( x ) = x ^ { 2 } - 2 x + 35$ 
B)  $f ( x ) = x ^ { 2 } + 2 x + 35$ 
C)  $f ( x ) = - x ^ { 2 } - 2 x - 35$ 
D)  $f ( x ) = - x ^ { 2 } + 2 x - 35$ 
E)  $f ( x ) = x ^ { 2 } + 2 x - 35$ 
A)  $f ( x ) = x ^ { 2 } - 2 x + 35$ 
B)  $f ( x ) = x ^ { 2 } + 2 x + 35$ 
C)  $f ( x ) = - x ^ { 2 } - 2 x - 35$ 
D)  $f ( x ) = - x ^ { 2 } + 2 x - 35$ 
E)  $f ( x ) = x ^ { 2 } + 2 x - 35$

Question 2

Determine the zeros (if any) of the rational function $g ( x ) = \frac { x ^ { 3 } - 8 } { x ^ { 2 } + 6 }$ .

Accepted Answer

A) x = -2, x = 2 
B) x = 2 
C)  $x = - \sqrt { 6 } , x = \sqrt { 6 } , x = 2$ 
D)  $x = - \sqrt { 6 } , x = \sqrt { 6 } , x = - 2 , x = 2$ 
E) no zeros 
A) x = -2, x = 2 
B) x = 2 
C)  $x = - \sqrt { 6 } , x = \sqrt { 6 } , x = 2$ 
D)  $x = - \sqrt { 6 } , x = \sqrt { 6 } , x = - 2 , x = 2$ 
E) no zeros

Question 3

Select the graph of $y = x ^ { 5 }$ and the transformation $f ( x ) = 1 - \frac { 1 } { 2 } x ^ { 5 }$ .

Accepted Answer

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

Question 4

the solution set of the inequality $\frac { 7 } { 2 } x ^ { 2 } + 7 x + 14 \geq 0$ is the entire set of real numbers.

Accepted Answer

A) True 
 B)False

Question 5

Use synthetic division to divide. 
 $\left( 4 x ^ { 3 } - 8 x + 24 x ^ { 2 } - 48 \right) \div ( x + 6 )$

Accepted Answer

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

Question 6

Perform the operation and write the result in standard form. 
 $( 1 + i ) ( 9 - 8 i )$

Accepted Answer

A)  $18 + i$ 
B)  $17 + i$ 
C)  $19 + i$ 
D)  $21 + i$ 
E)  $20 + i$ 
A)  $18 + i$ 
B)  $17 + i$ 
C)  $19 + i$ 
D)  $21 + i$ 
E)  $20 + i$

Question 7

Use the zero or root feature of a graphing utility to approximate the zeros of the function f(x) = x6 - 9x4 + 11x2 + 21 accurate to the nearest thousandth.

Accepted Answer

A) 2.646, 1.732 
B) ±1, -2.646, 1.732 
C) ±i, -2.646, -1.732 
D) ±1, 2.646, 1.732 
E) ±i, ±2.646, ±1.732 
A) 2.646, 1.732 
B) ±1, -2.646, 1.732 
C) ±i, -2.646, -1.732 
D) ±1, 2.646, 1.732 
E) ±i, ±2.646, ±1.732

Question 8

Solve the inequality and write the solution set in interval notation. 
 $6 x ^ { 2 } - 10 x < 0$

Accepted Answer

A)  $( - \infty , 0 ) ] \cup [$ $\frac { 5 } { 3 }$ $, \infty )$ 
B)  $\varnothing$ 
C)  $( - \infty , 0 )$ $\frac { 5 } { 3 }$ $, \infty )$ 
D)  $( \infty , 0 ) \cup [ -$ $\frac { 5 } { 3 }$ $, \infty )$ 
E)  $( 0 ,$ $\frac { 5 } { 3 }$ ) 
A)  $( - \infty , 0 ) ] \cup [$ $\frac { 5 } { 3 }$ $, \infty )$ 
B)  $\varnothing$ 
C)  $( - \infty , 0 )$ $\frac { 5 } { 3 }$ $, \infty )$ 
D)  $( \infty , 0 ) \cup [ -$ $\frac { 5 } { 3 }$ $, \infty )$ 
E)  $( 0 ,$ $\frac { 5 } { 3 }$ )

Question 9

Select the correct graph of the following function.   $f ( x ) = \frac { x ^ { 2 } - 9 } { x }$

Accepted Answer

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

Question 10

Find a polynomial with the given zeros.  $1,1,7$

Accepted Answer

A)  $9 x ^ { 2 } + 15 x - 7$ 
B)  $x ^ { 3 } + 9 x ^ { 2 } - 15 x + 7$ 
C)  $15 x ^ { 3 } - 9 x ^ { 2 } + 15 x - 7$ 
D)  $x ^ { 3 } - 9 x ^ { 2 } + 15 x - 7$ 
E) none of these 
A)  $9 x ^ { 2 } + 15 x - 7$ 
B)  $x ^ { 3 } + 9 x ^ { 2 } - 15 x + 7$ 
C)  $15 x ^ { 3 } - 9 x ^ { 2 } + 15 x - 7$ 
D)  $x ^ { 3 } - 9 x ^ { 2 } + 15 x - 7$ 
E) none of these

Question 11

Write the standard form of the equation of the parabola that has a vertex at (-6, -5) and passes through the point (-8, 6).

Accepted Answer

A)   $f ( x ) = \frac { 11 } { 36 } ( x - 6 ) ^ { 2 } - 5$ 
B)   $f ( x ) = - \frac { 5 } { 36 } ( x + 5 ) ^ { 2 } + 8$ 
C)   $f ( x ) = \frac { 11 } { 4 } ( x + 6 ) ^ { 2 } - 5$ 
D)   $f ( x ) = \frac { 3 } { 2 } ( x + 6 ) ^ { 2 } - 8$ 
E)   $f ( x ) = \frac { 5 } { 8 } ( x + 5 ) ^ { 2 } + 6$ 
A)   $f ( x ) = \frac { 11 } { 36 } ( x - 6 ) ^ { 2 } - 5$ 
B)   $f ( x ) = - \frac { 5 } { 36 } ( x + 5 ) ^ { 2 } + 8$ 
C)   $f ( x ) = \frac { 11 } { 4 } ( x + 6 ) ^ { 2 } - 5$ 
D)   $f ( x ) = \frac { 3 } { 2 } ( x + 6 ) ^ { 2 } - 8$ 
E)   $f ( x ) = \frac { 5 } { 8 } ( x + 5 ) ^ { 2 } + 6$

Question 12

Find domain of the following function. $g ( x ) = \frac { x ^ { 2 } - 4 } { x ^ { 2 } - 3 x + 2 }$

Accepted Answer

A) all real numbers x except x = -4 and x = -1 
B) all real numbers x except x = -3 and x = 2 
C) all real numbers x except x = 3 and x = 4 
D) all real numbers x except x = 2 and x = 1 
E) all real numbers x except x = -2 and x = 1 
A) all real numbers x except x = -4 and x = -1 
B) all real numbers x except x = -3 and x = 2 
C) all real numbers x except x = 3 and x = 4 
D) all real numbers x except x = 2 and x = 1 
E) all real numbers x except x = -2 and x = 1

Question 13

Select the graph of $y = x ^ { 3 }$ and the transformation $f ( x ) = ( x - 3 ) ^ { 3 }$ .

Accepted Answer

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

Question 14

Find all intercepts of the following function. 
 $g ( x ) = \frac { - 1 } { x + 3 }$

Accepted Answer

A) x-intercept: $\left( - \frac { 1 } { 3 } , 0 \right)$ 
B) y-intercept: $\left( 0 , - \frac { 1 } { 3 } \right)$ 
C) x-intercept: $\left( - \frac { 1 } { 3 } , 0 \right)$ and y-intercept: $\left( 0 , - \frac { 1 } { 3 } \right)$ 
D) x-intercept: $\left( \frac { 1 } { 3 } , 0 \right)$ 
E) y-intercept: $\left( 0 , \frac { 1 } { 3 } \right)$ 
A) x-intercept: $\left( - \frac { 1 } { 3 } , 0 \right)$ 
B) y-intercept: $\left( 0 , - \frac { 1 } { 3 } \right)$ 
C) x-intercept: $\left( - \frac { 1 } { 3 } , 0 \right)$ and y-intercept: $\left( 0 , - \frac { 1 } { 3 } \right)$ 
D) x-intercept: $\left( \frac { 1 } { 3 } , 0 \right)$ 
E) y-intercept: $\left( 0 , \frac { 1 } { 3 } \right)$

Question 15

Determine the zeros (if any) of the rational function $f ( x ) = \frac { x ^ { 2 } - 4 } { x + 3 }$ .

Accepted Answer

A) no zeros 
B)  $x = - \frac { 2 } { 3 } , x = \frac { 2 } { 3 }$ 
C)  x = -3 
D)  x = -4,  x = 4 
E)  x = -2,  x = 2 
A) no zeros 
B)  $x = - \frac { 2 } { 3 } , x = \frac { 2 } { 3 }$ 
C)  x = -3 
D)  x = -4,  x = 4 
E)  x = -2,  x = 2

Question 16

Given $f ( x ) = \frac { 11 x + 8 } { 11 x ^ { 2 } + 8 x } , g ( x ) = \frac { 1 } { x }$ .Determine the domains of f(x) and g(x).

Accepted Answer

A) Domain of f(x): all real numbers except 11 and $\frac { 8 } { 11 }$ Domain of g(x): all real numbers except 0 
B) Domain of f(x): all real numbers except $- \frac { 8 } { 11 }$ Domain of g(x): all real numbers except 1 
C) Domain of f(x): all real numbersDomain of g(x): all real numbers 
D) Domain of f(x): all real numbers except $- \frac { 11 } { 8 }$ Domain of g(x): all real numbers except 0 
E) Domain of f(x): all real numbers except 0 and $- \frac { 8 } { 11 }$ Domain of g(x): all real numbers except 0 
A) Domain of f(x): all real numbers except 11 and $\frac { 8 } { 11 }$ Domain of g(x): all real numbers except 0 
B) Domain of f(x): all real numbers except $- \frac { 8 } { 11 }$ Domain of g(x): all real numbers except 1 
C) Domain of f(x): all real numbersDomain of g(x): all real numbers 
D) Domain of f(x): all real numbers except $- \frac { 11 } { 8 }$ Domain of g(x): all real numbers except 0 
E) Domain of f(x): all real numbers except 0 and $- \frac { 8 } { 11 }$ Domain of g(x): all real numbers except 0

Question 17

Find two positive real numbers whose product is a maximum. ​
The sum of the first and three times the second is 48.
​

Accepted Answer

A) 24, 8 
B) 24, 16 
C) 16, 4 
D) 24, 6 
E) 42, 6 
A) 24, 8 
B) 24, 16 
C) 16, 4 
D) 24, 6 
E) 42, 6

Question 18

Find all the real zeros of $f ( x ) = 4 x ^ { 3 } - 20 x ^ { 2 } + 17 x - 4$ .

Accepted Answer

A) x = $\frac { 1 } { 2 }$ , 4 
B) x = $- \frac { 1 } { 2 }$ , $- \frac { 1 } { 4 }$ 
C) x = $\frac { 1 } { 4 }$ , -2 
D) x = $\frac { 1 } { 2 }$ , $- \frac { 1 } { 4 }$ 
E) x = $\frac { 1 } { 2 }$ , -4 
A) x = $\frac { 1 } { 2 }$ , 4 
B) x = $- \frac { 1 } { 2 }$ , $- \frac { 1 } { 4 }$ 
C) x = $\frac { 1 } { 4 }$ , -2 
D) x = $\frac { 1 } { 2 }$ , $- \frac { 1 } { 4 }$ 
E) x = $\frac { 1 } { 2 }$ , -4

Question 19

Use the given zero to find all the zeros of the function. ​
Function Zero
X3 - 3x2 + 16x - 48 4i
​

Accepted Answer

A) ±4i, ±3 
B) ±4i, -3 
C) ±4i, 3 
D) 4, ±3 
E) ±4i, ±4 
A) ±4i, ±3 
B) ±4i, -3 
C) ±4i, 3 
D) 4, ±3 
E) ±4i, ±4

Question 20

Use the position equation $s = - 16 t ^ { 2 } + v _ { 0 } t + s _ { 0 }$ , where s represents the height of an object (in feet), $v _ { 0 }$ represents the initial velocity of the object (in feet per second), $s_0$ represents the initial height of the object (in feet), and t represents the time (in seconds). A projectile is fired straight upward from ground level $\left( s _ { 0 } = 0 \right)$ with an initial velocity of 160 feet per second.At what instant will it be back at ground level?

Accepted Answer

A)  $t = 8$ Sec 
B)  $t = 10$ Sec 
C)  $t = 12$ Sec 
D)  $t = 11$ Sec 
E)  $t = 9$ Sec 
A)  $t = 8$ Sec 
B)  $t = 10$ Sec 
C)  $t = 12$ Sec 
D)  $t = 11$ Sec 
E)  $t = 9$ Sec

Select from the following which is the polynomial function that has the given zeros. $5 , - 7$

Determine the zeros (if any) of the rational function $g ( x ) = \frac { x ^ { 3 } - 8 } { x ^ { 2 } + 6 }$ .

Select the graph of $y = x ^ { 5 }$ and the transformation $f ( x ) = 1 - \frac { 1 } { 2 } x ^ { 5 }$ .

the solution set of the inequality $\frac { 7 } { 2 } x ^ { 2 } + 7 x + 14 \geq 0$ is the entire set of real numbers.

Use synthetic division to divide. $\left( 4 x ^ { 3 } - 8 x + 24 x ^ { 2 } - 48 \right) \div ( x + 6 )$

Perform the operation and write the result in standard form. $( 1 + i ) ( 9 - 8 i )$

Use the zero or root feature of a graphing utility to approximate the zeros of the function f(x) = x⁶ - 9x⁴ + 11x² + 21 accurate to the nearest thousandth.

Solve the inequality and write the solution set in interval notation. $6 x ^ { 2 } - 10 x < 0$

Select the correct graph of the following function. $f ( x ) = \frac { x ^ { 2 } - 9 } { x }$

Find a polynomial with the given zeros. $1,1,7$

Write the standard form of the equation of the parabola that has a vertex at (-6, -5) and passes through the point (-8, 6).

Find domain of the following function. $g ( x ) = \frac { x ^ { 2 } - 4 } { x ^ { 2 } - 3 x + 2 }$

Select the graph of $y = x ^ { 3 }$ and the transformation $f ( x ) = ( x - 3 ) ^ { 3 }$ .

Find all intercepts of the following function. $g ( x ) = \frac { - 1 } { x + 3 }$

Determine the zeros (if any) of the rational function $f ( x ) = \frac { x ^ { 2 } - 4 } { x + 3 }$ .

Given $f ( x ) = \frac { 11 x + 8 } { 11 x ^ { 2 } + 8 x } , g ( x ) = \frac { 1 } { x }$ .Determine the domains of f(x) and g(x).

Find two positive real numbers whose product is a maximum. The sum of the first and three times the second is 48.

Find all the real zeros of $f ( x ) = 4 x ^ { 3 } - 20 x ^ { 2 } + 17 x - 4$ .

Use the given zero to find all the zeros of the function. Function Zero X³ - 3x² + 16x - 48 4i

Functions and Their Graphs

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Additional Topics In Trigonometery

Systems Of Equations and Inequalities

Matrices and Determinants

Sequences Series and Probability

Topics In Analytic Geometry

Analytic Geometry In Three Dimensions

Limits and An Introduction To Calculus

Filters

Exam 2: Polynomial and Rational Functions

Select from the following which is the polynomial function that has the given zeros. 5,−75 , - 75,−7

Determine the zeros (if any) of the rational function g(x)=x3−8x2+6g ( x ) = \frac { x ^ { 3 } - 8 } { x ^ { 2 } + 6 }g(x)=x2+6x3−8​ .

Select the graph of y=x5y = x ^ { 5 }y=x5 and the transformation f(x)=1−12x5f ( x ) = 1 - \frac { 1 } { 2 } x ^ { 5 }f(x)=1−21​x5 .

the solution set of the inequality 72x2+7x+14≥0\frac { 7 } { 2 } x ^ { 2 } + 7 x + 14 \geq 027​x2+7x+14≥0 is the entire set of real numbers.

Use synthetic division to divide. (4x3−8x+24x2−48)÷(x+6)\left( 4 x ^ { 3 } - 8 x + 24 x ^ { 2 } - 48 \right) \div ( x + 6 )(4x3−8x+24x2−48)÷(x+6)

Perform the operation and write the result in standard form. (1+i)(9−8i)( 1 + i ) ( 9 - 8 i )(1+i)(9−8i)

Use the zero or root feature of a graphing utility to approximate the zeros of the function f(x) = x6 - 9x4 + 11x2 + 21 accurate to the nearest thousandth.

Solve the inequality and write the solution set in interval notation. 6x2−10x<06 x ^ { 2 } - 10 x < 06x2−10x<0

Select the correct graph of the following function. f(x)=x2−9xf ( x ) = \frac { x ^ { 2 } - 9 } { x }f(x)=xx2−9​

Find a polynomial with the given zeros. 1,1,71,1,71,1,7

Write the standard form of the equation of the parabola that has a vertex at (-6, -5) and passes through the point (-8, 6).

Find domain of the following function. g(x)=x2−4x2−3x+2g ( x ) = \frac { x ^ { 2 } - 4 } { x ^ { 2 } - 3 x + 2 }g(x)=x2−3x+2x2−4​

Select the graph of y=x3y = x ^ { 3 }y=x3 and the transformation f(x)=(x−3)3f ( x ) = ( x - 3 ) ^ { 3 }f(x)=(x−3)3 .

Find all intercepts of the following function. g(x)=−1x+3g ( x ) = \frac { - 1 } { x + 3 }g(x)=x+3−1​

Determine the zeros (if any) of the rational function f(x)=x2−4x+3f ( x ) = \frac { x ^ { 2 } - 4 } { x + 3 }f(x)=x+3x2−4​ .

Given f(x)=11x+811x2+8x,g(x)=1xf ( x ) = \frac { 11 x + 8 } { 11 x ^ { 2 } + 8 x } , g ( x ) = \frac { 1 } { x }f(x)=11x2+8x11x+8​,g(x)=x1​ .Determine the domains of f(x) and g(x).

Find two positive real numbers whose product is a maximum. ​ The sum of the first and three times the second is 48. ​

Find all the real zeros of f(x)=4x3−20x2+17x−4f ( x ) = 4 x ^ { 3 } - 20 x ^ { 2 } + 17 x - 4f(x)=4x3−20x2+17x−4 .

Use the given zero to find all the zeros of the function. ​ Function Zero X3 - 3x2 + 16x - 48 4i ​

Functions and Their Graphs

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Additional Topics In Trigonometery

Systems Of Equations and Inequalities

Matrices and Determinants

Sequences Series and Probability

Topics In Analytic Geometry

Analytic Geometry In Three Dimensions

Limits and An Introduction To Calculus

Filters

Select from the following which is the polynomial function that has the given zeros. $5 , - 7$

Determine the zeros (if any) of the rational function $g ( x ) = \frac { x ^ { 3 } - 8 } { x ^ { 2 } + 6 }$ .

Select the graph of $y = x ^ { 5 }$ and the transformation $f ( x ) = 1 - \frac { 1 } { 2 } x ^ { 5 }$ .

the solution set of the inequality $\frac { 7 } { 2 } x ^ { 2 } + 7 x + 14 \geq 0$ is the entire set of real numbers.

Use synthetic division to divide. $\left( 4 x ^ { 3 } - 8 x + 24 x ^ { 2 } - 48 \right) \div ( x + 6 )$

Perform the operation and write the result in standard form. $( 1 + i ) ( 9 - 8 i )$

Use the zero or root feature of a graphing utility to approximate the zeros of the function f(x) = x⁶ - 9x⁴ + 11x² + 21 accurate to the nearest thousandth.

Solve the inequality and write the solution set in interval notation. $6 x ^ { 2 } - 10 x < 0$

Select the correct graph of the following function. $f ( x ) = \frac { x ^ { 2 } - 9 } { x }$

Find a polynomial with the given zeros. $1,1,7$

Find domain of the following function. $g ( x ) = \frac { x ^ { 2 } - 4 } { x ^ { 2 } - 3 x + 2 }$

Select the graph of $y = x ^ { 3 }$ and the transformation $f ( x ) = ( x - 3 ) ^ { 3 }$ .

Find all intercepts of the following function. $g ( x ) = \frac { - 1 } { x + 3 }$

Determine the zeros (if any) of the rational function $f ( x ) = \frac { x ^ { 2 } - 4 } { x + 3 }$ .

Given $f ( x ) = \frac { 11 x + 8 } { 11 x ^ { 2 } + 8 x } , g ( x ) = \frac { 1 } { x }$ .Determine the domains of f(x) and g(x).

Find two positive real numbers whose product is a maximum. The sum of the first and three times the second is 48.

Find all the real zeros of $f ( x ) = 4 x ^ { 3 } - 20 x ^ { 2 } + 17 x - 4$ .

Use the given zero to find all the zeros of the function. Function Zero X³ - 3x² + 16x - 48 4i