Question 1

Given $f ( x ) = \frac { x ^ { 2 } - 10 x + 21 } { x + 5 }$ , determine the equations of any slant and vertical asymptote.

Accepted Answer

A) slant: y = x + 9; vertical: x = -12 
B) slant: y = x - 15; vertical: none 
C) slant: y = x + 8; vertical: x = -4 
D) slant: y = x - 15; vertical: x = -5 
E) slant: y = x + 8; vertical: x = -8 
A) slant: y = x + 9; vertical: x = -12 
B) slant: y = x - 15; vertical: none 
C) slant: y = x + 8; vertical: x = -4 
D) slant: y = x - 15; vertical: x = -5 
E) slant: y = x + 8; vertical: x = -8

Question 2

Find the vertex of the parabola. y = x2 - 12x + 36

Accepted Answer

A) (6, 0) 
B) (0, 6) 
C) (-24, 0) 
D) (36, 0) 
E) (6, -24) 
A) (6, 0) 
B) (0, 6) 
C) (-24, 0) 
D) (36, 0) 
E) (6, -24)

Question 3

Use the zero or root feature of a graphing utility to approximate the zeros of $f ( x ) = 2 x ^ { 3 } + 8 x ^ { 2 } - 5 x - 7$ accurate to the nearest thousandth.

Accepted Answer

A) x = -8.492, -0.695, 1.186 
B) x = -4.692 
C) x = -3.575 
D)  x = -3.910, -0.763, 1.173 
E)  x = -4.388, -0.720, 1.108 
A) x = -8.492, -0.695, 1.186 
B) x = -4.692 
C) x = -3.575 
D)  x = -3.910, -0.763, 1.173 
E)  x = -4.388, -0.720, 1.108

Question 4

Select the graph of the function and determine the zeros of the polynomial.   $f ( x ) = x ^ { 3 } - 5 x ^ { 2 }$

Accepted Answer

A)   $0,5$   
B)   $0 , - 5$   
C)   $0,5$   
D)   $0,5 , - 5$   
E)  $0,5 , - 5$   
A)   $0,5$   
B)   $0 , - 5$   
C)   $0,5$   
D)   $0,5 , - 5$   
E)  $0,5 , - 5$

Question 5

Determine the number of turning points of the graph of the function. 
 $f ( x ) = 2 x ^ { 4 } + 4 x ^ { 2 } + 4$

Accepted Answer

A) Number of turning points: 3 
B) Number of turning points: 1 
C) Number of turning points: 5 
D) Number of turning points: 2 
E) Number of turning points: 4 
A) Number of turning points: 3 
B) Number of turning points: 1 
C) Number of turning points: 5 
D) Number of turning points: 2 
E) Number of turning points: 4

Question 6

Select the graph of the function and determine the zeros of the polynomial. 
 $f ( t ) = \frac { 1 } { 6 } \left( t ^ { 2 } - 2 t + 20 \right)$

Accepted Answer

A)  No zeros    
B)  No zeros   
C)   $0,10 , - 10$   
D)  No zeros   
E)   $10 , - 10$   
A)  No zeros    
B)  No zeros   
C)   $0,10 , - 10$   
D)  No zeros   
E)   $10 , - 10$

Question 7

Use long division to divide. $\left( x ^ { 3 } + 4 x ^ { 2 } + x + 4 \right) \div ( x + 4 )$

Accepted Answer

A)  $x ^ { 2 } + 1$ 
B)  $x ^ { 2 } + 8 x + 33 - \frac { 129 } { x + 4 }$ 
C)  $x ^ { 2 } - 4$ 
D)  $x ^ { 2 } + 8 x + 33 + \frac { 120 } { x + 4 }$ 
E)  $x ^ { 2 } + 8 x + 33$ 
A)  $x ^ { 2 } + 1$ 
B)  $x ^ { 2 } + 8 x + 33 - \frac { 129 } { x + 4 }$ 
C)  $x ^ { 2 } - 4$ 
D)  $x ^ { 2 } + 8 x + 33 + \frac { 120 } { x + 4 }$ 
E)  $x ^ { 2 } + 8 x + 33$

Question 8

Simplify the rational expression, $\frac { 4 x ^ { 3 } + x ^ { 2 } - 51 x + 36 } { 4 x - 3 }$ , by using long division or synthetic division.

Accepted Answer

A)  $x ^ { 2 } + 7 x + 16$ 
B)  $x ^ { 2 } - 7 x - 12$ 
C)  $x ^ { 2 } - 6 x + 12$ 
D)  $x ^ { 2 } + 8 x + 9$ 
E)  $x ^ { 2 } + x - 12$ 
A)  $x ^ { 2 } + 7 x + 16$ 
B)  $x ^ { 2 } - 7 x - 12$ 
C)  $x ^ { 2 } - 6 x + 12$ 
D)  $x ^ { 2 } + 8 x + 9$ 
E)  $x ^ { 2 } + x - 12$

Question 9

Find the vertex of the parabola. ​
Y = 3x2 - 1
​

Accepted Answer

A) (-1, 3) 
B) (0, -1) 
C) (3, -1) 
D) (-1, 0) 
E) (0, 3) 
A) (-1, 3) 
B) (0, -1) 
C) (3, -1) 
D) (-1, 0) 
E) (0, 3)

Question 10

Find the domain of x in the expression.  
$\sqrt { x ^ { 2 } - 7 x + 12 }$

Accepted Answer

A)  $( - \infty , 3 ] \cup [ 4 , \infty )$ 
B)  $( - \infty , 3 ] \cap [ 4 , \infty )$ 
C)  $( \infty , - 3 ] \cup [ 4 , \infty )$ 
D)  $( \infty , 3 ] \cap [ 4 , \infty )$ 
E)  $( \infty , - 3 ] \cap [ 4 , \infty )$ 
A)  $( - \infty , 3 ] \cup [ 4 , \infty )$ 
B)  $( - \infty , 3 ] \cap [ 4 , \infty )$ 
C)  $( \infty , - 3 ] \cup [ 4 , \infty )$ 
D)  $( \infty , 3 ] \cap [ 4 , \infty )$ 
E)  $( \infty , - 3 ] \cap [ 4 , \infty )$

Question 11

A roofing contractor is fabricating gutters from $10$ -inch aluminum sheeting.The contractor plans to use an aluminum siding folding press to create the gutter by creasing equal lengths for the sidewalls (see figure).     where $a = 10 - 2 x$ Let x represent the height of the sidewall of the gutter.Write a function A that represents the
Cross-sectional area of the gutter.

Accepted Answer

A)  $A = - 2 x ^ { 2 } + 10 x$ 
B)  $A = 10 x ^ { 2 } - 2 x$ 
C)  $A = - 10 x - 2 x ^ { 2 }$ 
D)  $A = 2 x ^ { 2 } - 10 x$ 
E)  $A = 2 x ^ { 2 } + 10 x$ 
A)  $A = - 2 x ^ { 2 } + 10 x$ 
B)  $A = 10 x ^ { 2 } - 2 x$ 
C)  $A = - 10 x - 2 x ^ { 2 }$ 
D)  $A = 2 x ^ { 2 } - 10 x$ 
E)  $A = 2 x ^ { 2 } + 10 x$

Question 12

The function given by $f ( x ) = - 16 x ^ { 2 } - 7$ has no x-intercepts.

Accepted Answer

A) True 
 B)False

Question 13

Find the domain of the function.  
  $g ( s ) = \frac { - 3 s } { s - 9 }$

Accepted Answer

A) s = 9 
B) all real numbers s $\neq$  9, s $\neq$0 
C)  s = 9, s = 0 
D) all real numbers s $\neq$   9 
E)  $\varnothing$ 
A) s = 9 
B) all real numbers s $\neq$  9, s $\neq$0 
C)  s = 9, s = 0 
D) all real numbers s $\neq$   9 
E)  $\varnothing$

Question 14

Find the inverse of the one-to-one function. 
 $y = 7 x + 5$

Accepted Answer

A)  $y = \frac { x - 7 } { 5 }$ 
B)  $y = \frac { x - 5 } { 7 }$ 
C)  $y = \frac { 7 } { x - 5 }$ 
D)  $y = \frac { x + 5 } { 7 }$ 
E) none of the above 
A)  $y = \frac { x - 7 } { 5 }$ 
B)  $y = \frac { x - 5 } { 7 }$ 
C)  $y = \frac { 7 } { x - 5 }$ 
D)  $y = \frac { x + 5 } { 7 }$ 
E) none of the above

Question 15

Using the factors (5x + 4) and (x - 1), find the remaining factor(s) of $f ( x ) = - 20 x ^ { 4 } + 109 x ^ { 3 } - 30 x ^ { 2 } - 79 x + 20$ and write the polynomial in fully factored form.

Accepted Answer

A)   $f ( x ) = ( 5 x + 4 ) ( - x + 5 ) ( 4 x - 1 ) ( x - 1 )$ 
B)   $f ( x ) = ( 5 x + 4 ) ^ { 2 } ( 4 x - 1 ) ( x + 1 )$ 
C)   $f ( x ) = ( 5 x + 4 ) ( 5 x + 4 ) ( 4 x - 1 ) ( x - 1 )$ 
D)   $f ( x ) = ( 5 x + 4 ) ^ { 2 } ( x - 1 ) ^ { 2 }$ 
E)   $f ( x ) = ( 5 x + 4 ) ( - x - 5 ) ^ { 2 } ( x + 1 )$ 
A)   $f ( x ) = ( 5 x + 4 ) ( - x + 5 ) ( 4 x - 1 ) ( x - 1 )$ 
B)   $f ( x ) = ( 5 x + 4 ) ^ { 2 } ( 4 x - 1 ) ( x + 1 )$ 
C)   $f ( x ) = ( 5 x + 4 ) ( 5 x + 4 ) ( 4 x - 1 ) ( x - 1 )$ 
D)   $f ( x ) = ( 5 x + 4 ) ^ { 2 } ( x - 1 ) ^ { 2 }$ 
E)   $f ( x ) = ( 5 x + 4 ) ( - x - 5 ) ^ { 2 } ( x + 1 )$

Question 16

A rectangular package to be sent by a delivery service can have a maximum combined length and girth (perimeter of a cross section) of 168 inches. ​   ​
Write a function that represents the volume of the package.
​

Accepted Answer

A) V(x) = - 4x2(42 + x) 
B) V(x) = 4x2(42 + x) 
C) V(x) = 4x2(42 - x) 
D) V(x) = 4x2(-42 - x) 
E) V(x) = - 4x2(42 - x) 
A) V(x) = - 4x2(42 + x) 
B) V(x) = 4x2(42 + x) 
C) V(x) = 4x2(42 - x) 
D) V(x) = 4x2(-42 - x) 
E) V(x) = - 4x2(42 - x)

Question 17

Simplify the complex number and write it in standard form.  
  $( 2 i ) ^ { 4 }$

Accepted Answer

A)  16 
B)  -16 
C)  16i 
D)  -16i 
E)  2i 
A)  16 
B)  -16 
C)  16i 
D)  -16i 
E)  2i

Question 18

Find domain of the following function. $g ( x ) = \frac { x ^ { 2 } - 49 } { x ^ { 2 } - 6 x - 7 }$

Accepted Answer

A) all real numbers x except x = -49 and x = -1 
B) all real numbers x except x = -6 and x =  7 
C) all real numbers x except x = 6 and x = 49 
D) all real numbers x except x = 7 and x = -1 
E) all real numbers x except x = -7 and x = 1 
A) all real numbers x except x = -49 and x = -1 
B) all real numbers x except x = -6 and x =  7 
C) all real numbers x except x = 6 and x = 49 
D) all real numbers x except x = 7 and x = -1 
E) all real numbers x except x = -7 and x = 1

Question 19

Do the operation and express the answer in a + bi form. 
 $\frac { - 19 } { i ^ { 36 } }$

Accepted Answer

A) 19i 
B) - 19i 
C) - 190i 
D) - 19 
E) 19 
A) 19i 
B) - 19i 
C) - 190i 
D) - 19 
E) 19

Question 20

Use a graphing utility to graph the equation.Use the graph to approximate the values of x that satisfy each inequality.  
Equation: $y = \frac { 6 x } { x - 5 }$  
Inequality: $y \geq 8$

Accepted Answer

A)     $5 < x \leq - \frac { 10 } { 1 }$ 
B)    $5 < x \leq \frac { 10 } { 1 }$ 
C)    $5 < x$ 
D)    $5 < x \leq \frac { 10 } { 1 }$ 
E)    $6 < x \leq \frac { 10 } { 1 }$ 
A)     $5 < x \leq - \frac { 10 } { 1 }$ 
B)    $5 < x \leq \frac { 10 } { 1 }$ 
C)    $5 < x$ 
D)    $5 < x \leq \frac { 10 } { 1 }$ 
E)    $6 < x \leq \frac { 10 } { 1 }$

Given $f ( x ) = \frac { x ^ { 2 } - 10 x + 21 } { x + 5 }$ , determine the equations of any slant and vertical asymptote.

Find the vertex of the parabola. y = x² - 12x + 36

Use the zero or root feature of a graphing utility to approximate the zeros of $f ( x ) = 2 x ^ { 3 } + 8 x ^ { 2 } - 5 x - 7$ accurate to the nearest thousandth.

Select the graph of the function and determine the zeros of the polynomial. $f ( x ) = x ^ { 3 } - 5 x ^ { 2 }$

Determine the number of turning points of the graph of the function. $f ( x ) = 2 x ^ { 4 } + 4 x ^ { 2 } + 4$

Select the graph of the function and determine the zeros of the polynomial. $f ( t ) = \frac { 1 } { 6 } \left( t ^ { 2 } - 2 t + 20 \right)$

Use long division to divide. $\left( x ^ { 3 } + 4 x ^ { 2 } + x + 4 \right) \div ( x + 4 )$

Simplify the rational expression, $\frac { 4 x ^ { 3 } + x ^ { 2 } - 51 x + 36 } { 4 x - 3 }$ , by using long division or synthetic division.

Find the vertex of the parabola. Y = 3x² - 1

Find the domain of x in the expression. $\sqrt { x ^ { 2 } - 7 x + 12 }$

The function given by $f ( x ) = - 16 x ^ { 2 } - 7$ has no x-intercepts.

Find the domain of the function. $g ( s ) = \frac { - 3 s } { s - 9 }$

Find the inverse of the one-to-one function. $y = 7 x + 5$

Using the factors (5x + 4) and (x - 1), find the remaining factor(s) of $f ( x ) = - 20 x ^ { 4 } + 109 x ^ { 3 } - 30 x ^ { 2 } - 79 x + 20$ and write the polynomial in fully factored form.

A rectangular package to be sent by a delivery service can have a maximum combined length and girth (perimeter of a cross section) of 168 inches. Write a function that represents the volume of the package.

Simplify the complex number and write it in standard form. $( 2 i ) ^ { 4 }$

Find domain of the following function. $g ( x ) = \frac { x ^ { 2 } - 49 } { x ^ { 2 } - 6 x - 7 }$

Do the operation and express the answer in a + bi form. $\frac { - 19 } { i ^ { 36 } }$

Use a graphing utility to graph the equation.Use the graph to approximate the values of x that satisfy each inequality. Equation: $y = \frac { 6 x } { x - 5 }$ Inequality: $y \geq 8$

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

Given f(x)=x2−10x+21x+5f ( x ) = \frac { x ^ { 2 } - 10 x + 21 } { x + 5 }f(x)=x+5x2−10x+21​ , determine the equations of any slant and vertical asymptote.

Find the vertex of the parabola. y = x2 - 12x + 36

Use the zero or root feature of a graphing utility to approximate the zeros of f(x)=2x3+8x2−5x−7f ( x ) = 2 x ^ { 3 } + 8 x ^ { 2 } - 5 x - 7f(x)=2x3+8x2−5x−7 accurate to the nearest thousandth.

Select the graph of the function and determine the zeros of the polynomial. f(x)=x3−5x2f ( x ) = x ^ { 3 } - 5 x ^ { 2 }f(x)=x3−5x2

Determine the number of turning points of the graph of the function. f(x)=2x4+4x2+4f ( x ) = 2 x ^ { 4 } + 4 x ^ { 2 } + 4f(x)=2x4+4x2+4

Select the graph of the function and determine the zeros of the polynomial. f(t)=16(t2−2t+20)f ( t ) = \frac { 1 } { 6 } \left( t ^ { 2 } - 2 t + 20 \right)f(t)=61​(t2−2t+20)

Use long division to divide. (x3+4x2+x+4)÷(x+4)\left( x ^ { 3 } + 4 x ^ { 2 } + x + 4 \right) \div ( x + 4 )(x3+4x2+x+4)÷(x+4)

Simplify the rational expression, 4x3+x2−51x+364x−3\frac { 4 x ^ { 3 } + x ^ { 2 } - 51 x + 36 } { 4 x - 3 }4x−34x3+x2−51x+36​ , by using long division or synthetic division.

Find the vertex of the parabola. ​ Y = 3x2 - 1 ​

Find the domain of x in the expression. x2−7x+12\sqrt { x ^ { 2 } - 7 x + 12 }x2−7x+12​

The function given by f(x)=−16x2−7f ( x ) = - 16 x ^ { 2 } - 7f(x)=−16x2−7 has no x-intercepts.

Find the domain of the function. g(s)=−3ss−9g ( s ) = \frac { - 3 s } { s - 9 }g(s)=s−9−3s​

Find the inverse of the one-to-one function. y=7x+5y = 7 x + 5y=7x+5

Using the factors (5x + 4) and (x - 1), find the remaining factor(s) of f(x)=−20x4+109x3−30x2−79x+20f ( x ) = - 20 x ^ { 4 } + 109 x ^ { 3 } - 30 x ^ { 2 } - 79 x + 20f(x)=−20x4+109x3−30x2−79x+20 and write the polynomial in fully factored form.

A rectangular package to be sent by a delivery service can have a maximum combined length and girth (perimeter of a cross section) of 168 inches. ​ ​ Write a function that represents the volume of the package. ​

Simplify the complex number and write it in standard form. (2i)4( 2 i ) ^ { 4 }(2i)4

Find domain of the following function. g(x)=x2−49x2−6x−7g ( x ) = \frac { x ^ { 2 } - 49 } { x ^ { 2 } - 6 x - 7 }g(x)=x2−6x−7x2−49​

Do the operation and express the answer in a + bi form. −19i36\frac { - 19 } { i ^ { 36 } }i36−19​

Use a graphing utility to graph the equation.Use the graph to approximate the values of x that satisfy each inequality. Equation: y=6xx−5y = \frac { 6 x } { x - 5 }y=x−56x​ Inequality: y≥8y \geq 8y≥8

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

Given $f ( x ) = \frac { x ^ { 2 } - 10 x + 21 } { x + 5 }$ , determine the equations of any slant and vertical asymptote.

Find the vertex of the parabola. y = x² - 12x + 36

Use the zero or root feature of a graphing utility to approximate the zeros of $f ( x ) = 2 x ^ { 3 } + 8 x ^ { 2 } - 5 x - 7$ accurate to the nearest thousandth.

Select the graph of the function and determine the zeros of the polynomial. $f ( x ) = x ^ { 3 } - 5 x ^ { 2 }$

Determine the number of turning points of the graph of the function. $f ( x ) = 2 x ^ { 4 } + 4 x ^ { 2 } + 4$

Select the graph of the function and determine the zeros of the polynomial. $f ( t ) = \frac { 1 } { 6 } \left( t ^ { 2 } - 2 t + 20 \right)$

Use long division to divide. $\left( x ^ { 3 } + 4 x ^ { 2 } + x + 4 \right) \div ( x + 4 )$

Simplify the rational expression, $\frac { 4 x ^ { 3 } + x ^ { 2 } - 51 x + 36 } { 4 x - 3 }$ , by using long division or synthetic division.

Find the vertex of the parabola. Y = 3x² - 1

Find the domain of x in the expression. $\sqrt { x ^ { 2 } - 7 x + 12 }$

The function given by $f ( x ) = - 16 x ^ { 2 } - 7$ has no x-intercepts.

Find the domain of the function. $g ( s ) = \frac { - 3 s } { s - 9 }$

Find the inverse of the one-to-one function. $y = 7 x + 5$

Using the factors (5x + 4) and (x - 1), find the remaining factor(s) of $f ( x ) = - 20 x ^ { 4 } + 109 x ^ { 3 } - 30 x ^ { 2 } - 79 x + 20$ and write the polynomial in fully factored form.

A rectangular package to be sent by a delivery service can have a maximum combined length and girth (perimeter of a cross section) of 168 inches. Write a function that represents the volume of the package.

Simplify the complex number and write it in standard form. $( 2 i ) ^ { 4 }$

Find domain of the following function. $g ( x ) = \frac { x ^ { 2 } - 49 } { x ^ { 2 } - 6 x - 7 }$

Do the operation and express the answer in a + bi form. $\frac { - 19 } { i ^ { 36 } }$

Use a graphing utility to graph the equation.Use the graph to approximate the values of x that satisfy each inequality. Equation: $y = \frac { 6 x } { x - 5 }$ Inequality: $y \geq 8$