Question 1

Determine whether lines L1 and L2 passing through the pairs of points are parallel, perpendicular, or neither. L1 : (-5, -9), (-7, 2)
L2 : (-8, 1), (-19, -1)

Accepted Answer

A) parallel 
B) perpendicular 
C) neither 
A) parallel 
B) perpendicular 
C) neither

Question 2

Evaluate $( f - g ) ( 3 )$ where $f ( x ) = x ^ { 2 } + 5 x - 50$ and $g ( x ) = - 3 x - 8.$

Accepted Answer

A) -25 
B) -9 
C) -15 
D) -26 
E) -43 
A) -25 
B) -9 
C) -15 
D) -26 
E) -43

Question 3

Write the equation that expresses the relationship between the variables described below, then use the given data to solve for the variation of constant. "y varies directly as $z$ , and $y = 86.66$ when $z = 14.$ "

Accepted Answer

A)  $y = \frac { k } { z }$ ; $k = 1213.24$ 
B)  $y = \sqrt { k } z$ ; $k = 38.32$ 
C)  $y = k z$ ; $k = 6.19$ 
D)  $y = k ^ { 2 } z$ ; $k = 2.49$ 
E)  $y = \sqrt { k z }$ ; $k = 536.43$ 
A)  $y = \frac { k } { z }$ ; $k = 1213.24$ 
B)  $y = \sqrt { k } z$ ; $k = 38.32$ 
C)  $y = k z$ ; $k = 6.19$ 
D)  $y = k ^ { 2 } z$ ; $k = 2.49$ 
E)  $y = \sqrt { k z }$ ; $k = 536.43$

Question 4

Graph y as a function of x by finding the slope and y-intercept of the line below. $y = 3 x + 1$

Accepted Answer

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

Question 5

Suppose the average remaining lifetime for women in a given country is given in the following table. $$\begin{array} { | c | c | } 
\hline \text { Age } & \text { Years } \
\hline 5 & 72.4 \
\hline 25 & 53.1 \
\hline 30 & 49.5 \
\hline 35 & 44.5 \
\hline 40 & 39.2 \
\hline
\end{array}$$ Find the linear regression equation for these data, whose parameters are rounded to the nearest hundredth, where x is the age, in years, and A is the remaining lifetime, in years. Use the regression equation to estimate the remaining lifetime for a 31-year old woman.

Accepted Answer

A) 42.29 years 
B) 50.75 years 
C) 46.99 years 
D) 55.45 years 
E) 52.63 years 
A) 42.29 years 
B) 50.75 years 
C) 46.99 years 
D) 55.45 years 
E) 52.63 years

Question 6

Evaluate $( f g ) ( 2 )$ where $f ( x ) = x ^ { 2 } + 15 x + 54$ and $g ( x ) = - 10 x - 6.$

Accepted Answer

A) 2288 
B) 520 
C) -2288 
D) -392 
E) -1766 
A) 2288 
B) 520 
C) -2288 
D) -392 
E) -1766

Question 7

Find $f \circ g.$ f (x) = -5x - 9 g (x) = x + 5

Accepted Answer

A)  $( f \circ g ) ( x ) =$ -5x - 34 
B)  $( f \circ g ) ( x ) =$ -5x - 4 
C)  $( f \circ g ) ( x ) =$ -5x2 - 34x - 45 
D)  $( f \circ g ) ( x ) =$ -6x - 14 
E)  $( f \circ g ) ( x ) =$ -6x - 4 
A)  $( f \circ g ) ( x ) =$ -5x - 34 
B)  $( f \circ g ) ( x ) =$ -5x - 4 
C)  $( f \circ g ) ( x ) =$ -5x2 - 34x - 45 
D)  $( f \circ g ) ( x ) =$ -6x - 14 
E)  $( f \circ g ) ( x ) =$ -6x - 4

Question 8

Use a graphing utility to graph the function and determine whether the function is even, odd, or neither. $f ( x ) = x ^ { 2 } - x ^ { 4 }$

Accepted Answer

A) Neither even nor odd   
B) Odd   
C) Even   
D) Neither even nor odd   
E) Even   
A) Neither even nor odd   
B) Odd   
C) Even   
D) Neither even nor odd   
E) Even

Question 9

Find ( f F1F1F1S1?F1F1F10 g )(x). $f ( x ) = \frac { 2 x } { 6 x + 9 }$ $g ( x ) = - \frac { 9 } { x }$

Accepted Answer

A)  $( f - g ) ( x ) = \frac { 2 x + 9 } { 5 x + 9 }$ 
B)  $( f - g ) ( x ) = \frac { 2 x + 63 } { 6 x + 9 }$ 
C)  $( f - g ) ( x ) = \frac { 2 x + 45 } { 6 x + 9 }$ 
D)  $( f - g ) ( x ) = \frac { 2 x ^ { 2 } + 54 x - 81 } { 6 x ^ { 2 } + 9 x }$ 
E)  $( f - g ) ( x ) = \frac { 2 x ^ { 2 } + 54 x + 81 } { 6 x ^ { 2 } + 9 x }$ 
A)  $( f - g ) ( x ) = \frac { 2 x + 9 } { 5 x + 9 }$ 
B)  $( f - g ) ( x ) = \frac { 2 x + 63 } { 6 x + 9 }$ 
C)  $( f - g ) ( x ) = \frac { 2 x + 45 } { 6 x + 9 }$ 
D)  $( f - g ) ( x ) = \frac { 2 x ^ { 2 } + 54 x - 81 } { 6 x ^ { 2 } + 9 x }$ 
E)  $( f - g ) ( x ) = \frac { 2 x ^ { 2 } + 54 x + 81 } { 6 x ^ { 2 } + 9 x }$

Question 10

Given $y = \frac { x ^ { 3 } } { x ^ { 4 } + 1 }$ , use the algebraic tests to determine symmetry with respect to both axes and the origin.

Accepted Answer

A) y-axis symmetry only 
B) x-axis symmetry only 
C) origin symmetry only 
D) x-axis, y-axis, and origin symmetry 
E) no symmetry 
A) y-axis symmetry only 
B) x-axis symmetry only 
C) origin symmetry only 
D) x-axis, y-axis, and origin symmetry 
E) no symmetry

Question 11

Estimate the slope of the line.

Accepted Answer

A)  $- \frac { 1 } { 2 }$ 
B)  $2$ 
C)  $- 2$ 
D)  $\frac { 1 } { 2 }$ 
E)  $- 3$ 
A)  $- \frac { 1 } { 2 }$ 
B)  $2$ 
C)  $- 2$ 
D)  $\frac { 1 } { 2 }$ 
E)  $- 3$

Question 12

Find the distance between the points. Round to the nearest hundredth, if necessary. (-6, 2), (7, -4)

Accepted Answer

A) 2.24 
B) 6.08 
C) 14.32 
D) 13.15 
E) 13.6 
A) 2.24 
B) 6.08 
C) 14.32 
D) 13.15 
E) 13.6

Question 13

Describe the sequence of transformations from $f ( x ) = | x |$ to $g$ . Then sketch the graph of $g$ by hand. Verify with a graphing utility. $f ( x ) = | x | + 2$

Accepted Answer

A) Vertical shifts down 3 units   
B) Vertical shifts 2 units upward   
C) Horizontal shift 1 unit to the right   
D) Horizontal shifts 4 units to the left   
E) Vertical shifts 3 units upward   
A) Vertical shifts down 3 units   
B) Vertical shifts 2 units upward   
C) Horizontal shift 1 unit to the right   
D) Horizontal shifts 4 units to the left   
E) Vertical shifts 3 units upward

Question 14

Determine the domain of $f \circ g$ if $f ( x ) = x ^ { 2 } - 17$ and $g ( x ) = \sqrt { x }.$

Accepted Answer

A)  $( - \infty , \infty )$ 
B)  $( - \infty , - 17 ] \cup [ 17 , \infty )$ 
C)  $( - \infty , - \sqrt { 17 } ] \cup [ \sqrt { 17 } , \infty )$ 
D)  $[ \sqrt { 17 } , \infty )$ 
E)  $[ 0 , \infty )$ 
A)  $( - \infty , \infty )$ 
B)  $( - \infty , - 17 ] \cup [ 17 , \infty )$ 
C)  $( - \infty , - \sqrt { 17 } ] \cup [ \sqrt { 17 } , \infty )$ 
D)  $[ \sqrt { 17 } , \infty )$ 
E)  $[ 0 , \infty )$

Question 15

Sketch the graph of the function. $f ( x ) = $

Accepted Answer

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

Question 16

Match the equation below with its graph. $y = 4 + x$ Graph I :   Graph IV :   Graph II :   Graph V :   Graph III :

Accepted Answer

A) Graph IV 
B) Graph III 
C) Graph V 
D) Graph II 
E) Graph I 
A) Graph IV 
B) Graph III 
C) Graph V 
D) Graph II 
E) Graph I

Question 17

Sketch the graph of the equation below. $y = \sqrt { x + 1 }$

Accepted Answer

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

Question 18

Find the slope of the line that passes through the points $A ( - 4 , - 2 ) \text { and } B ( 10,9 ).$

Accepted Answer

A)  $\frac { 11 } { 14 }$ 
B)  $- \frac { 1 } { 2 }$ 
C)  $- \frac { 11 } { 14 }$ 
D)  $\frac { 13 } { 12 }$ 
E)  $\frac { 7 } { 6 }$ 
A)  $\frac { 11 } { 14 }$ 
B)  $- \frac { 1 } { 2 }$ 
C)  $- \frac { 11 } { 14 }$ 
D)  $\frac { 13 } { 12 }$ 
E)  $\frac { 7 } { 6 }$

Question 19

Find the slope and y-intercept of the equation of the line. -3y - 9x = -12

Accepted Answer

A) slope: 9; y-intercept: -12 
B) slope: -12; y-intercept: 9 
C) slope: 9; y-intercept: -3 
D) slope: 4; y-intercept: -3 
E) slope: -3; y-intercept: 4 
A) slope: 9; y-intercept: -12 
B) slope: -12; y-intercept: 9 
C) slope: 9; y-intercept: -3 
D) slope: 4; y-intercept: -3 
E) slope: -3; y-intercept: 4

Question 20

Use the graphs of f and g to evaluate the function.     $$( f \circ g ) ( 3 )$$

Accepted Answer

A) 1 
B) -2 
C) 4 
D) -1 
E) 2 
A) 1 
B) -2 
C) 4 
D) -1 
E) 2

Determine whether lines L1 and L2 passing through the pairs of points are parallel, perpendicular, or neither. L1 : (-5, -9), (-7, 2) L2 : (-8, 1), (-19, -1)

Evaluate $( f - g ) ( 3 )$ where $f ( x ) = x ^ { 2 } + 5 x - 50$ and $g ( x ) = - 3 x - 8.$

Write the equation that expresses the relationship between the variables described below, then use the given data to solve for the variation of constant. "y varies directly as $z$ , and $y = 86.66$ when $z = 14.$ "

Graph y as a function of x by finding the slope and y-intercept of the line below. $y = 3 x + 1$

Evaluate $( f g ) ( 2 )$ where $f ( x ) = x ^ { 2 } + 15 x + 54$ and $g ( x ) = - 10 x - 6.$

Find $f \circ g.$ f (x) = -5x - 9 g (x) = x + 5

Use a graphing utility to graph the function and determine whether the function is even, odd, or neither. $f ( x ) = x ^ { 2 } - x ^ { 4 }$

Find ( f ? g )(x). $f ( x ) = \frac { 2 x } { 6 x + 9 }$ $g ( x ) = - \frac { 9 } { x }$

Given $y = \frac { x ^ { 3 } } { x ^ { 4 } + 1 }$ , use the algebraic tests to determine symmetry with respect to both axes and the origin.

Estimate the slope of the line.

Find the distance between the points. Round to the nearest hundredth, if necessary. (-6, 2), (7, -4)

Describe the sequence of transformations from $f ( x ) = | x |$ to $g$ . Then sketch the graph of $g$ by hand. Verify with a graphing utility. $f ( x ) = | x | + 2$

Determine the domain of $f \circ g$ if $f ( x ) = x ^ { 2 } - 17$ and $g ( x ) = \sqrt { x }.$

Sketch the graph of the function. $f ( x ) =$

Match the equation below with its graph. $y = 4 + x$ Graph I : Graph IV : Graph II : Graph V : Graph III :

Sketch the graph of the equation below. $y = \sqrt { x + 1 }$

Find the slope of the line that passes through the points $A ( - 4 , - 2 ) \text { and } B ( 10,9 ).$

Find the slope and y-intercept of the equation of the line. -3y - 9x = -12

Use the graphs of f and g to evaluate the function. $Use the graphs of f and g to evaluate the function. ( f \circ g ) ( 3 )$ $Use the graphs of f and g to evaluate the function. ( f \circ g ) ( 3 )$ $( f \circ g ) ( 3 )$

Fundamental Concepts of Algebra

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Exam 3: Functions and Graphs

Determine whether lines L1 and L2 passing through the pairs of points are parallel, perpendicular, or neither. L1 : (-5, -9), (-7, 2) L2 : (-8, 1), (-19, -1)

Evaluate (f−g)(3)( f - g ) ( 3 )(f−g)(3) where f(x)=x2+5x−50f ( x ) = x ^ { 2 } + 5 x - 50f(x)=x2+5x−50 and g(x)=−3x−8.g ( x ) = - 3 x - 8.g(x)=−3x−8.

Write the equation that expresses the relationship between the variables described below, then use the given data to solve for the variation of constant. "y varies directly as zzz , and y=86.66y = 86.66y=86.66 when z=14.z = 14.z=14. "

Graph y as a function of x by finding the slope and y-intercept of the line below. y=3x+1y = 3 x + 1y=3x+1

Evaluate (fg)(2)( f g ) ( 2 )(fg)(2) where f(x)=x2+15x+54f ( x ) = x ^ { 2 } + 15 x + 54f(x)=x2+15x+54 and g(x)=−10x−6.g ( x ) = - 10 x - 6.g(x)=−10x−6.

Find f∘g.f \circ g.f∘g. f (x) = -5x - 9 g (x) = x + 5

Use a graphing utility to graph the function and determine whether the function is even, odd, or neither. f(x)=x2−x4f ( x ) = x ^ { 2 } - x ^ { 4 }f(x)=x2−x4

Find ( f ? g )(x). f(x)=2x6x+9f ( x ) = \frac { 2 x } { 6 x + 9 }f(x)=6x+92x​ g(x)=−9xg ( x ) = - \frac { 9 } { x }g(x)=−x9​

Given y=x3x4+1y = \frac { x ^ { 3 } } { x ^ { 4 } + 1 }y=x4+1x3​ , use the algebraic tests to determine symmetry with respect to both axes and the origin.

Estimate the slope of the line.

Find the distance between the points. Round to the nearest hundredth, if necessary. (-6, 2), (7, -4)

Describe the sequence of transformations from f(x)=∣x∣f ( x ) = | x |f(x)=∣x∣ to ggg . Then sketch the graph of ggg by hand. Verify with a graphing utility. f(x)=∣x∣+2f ( x ) = | x | + 2f(x)=∣x∣+2

Determine the domain of f∘gf \circ gf∘g if f(x)=x2−17f ( x ) = x ^ { 2 } - 17f(x)=x2−17 and g(x)=x.g ( x ) = \sqrt { x }.g(x)=x​.

Sketch the graph of the function. f(x)=f ( x ) = f(x)=

Match the equation below with its graph. y=4+xy = 4 + xy=4+x Graph I : Graph IV : Graph II : Graph V : Graph III :

Sketch the graph of the equation below. y=x+1y = \sqrt { x + 1 }y=x+1​

Find the slope of the line that passes through the points A(−4,−2) and B(10,9).A ( - 4 , - 2 ) \text { and } B ( 10,9 ).A(−4,−2) and B(10,9).

Find the slope and y-intercept of the equation of the line. -3y - 9x = -12

Use the graphs of f and g to evaluate the function. (f∘g)(3)( f \circ g ) ( 3 )(f∘g)(3)

Fundamental Concepts of Algebra

Equations and Inequalities

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Systems of Equations and Inequalities

Matrices and Determinants

Limits and Derivatives

Applications of the Derivative

Further Applications of the Derivative

Derivatives of Exponential and Logarithmic Functions

Integration and Its Applications

Techniques of Integration

Functions of Several Variables

Trigonometric Functions Web

Series and Taylor Polynomials Web

Probability Web

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Evaluate $( f - g ) ( 3 )$ where $f ( x ) = x ^ { 2 } + 5 x - 50$ and $g ( x ) = - 3 x - 8.$

Write the equation that expresses the relationship between the variables described below, then use the given data to solve for the variation of constant. "y varies directly as $z$ , and $y = 86.66$ when $z = 14.$ "

Graph y as a function of x by finding the slope and y-intercept of the line below. $y = 3 x + 1$

Evaluate $( f g ) ( 2 )$ where $f ( x ) = x ^ { 2 } + 15 x + 54$ and $g ( x ) = - 10 x - 6.$

Find $f \circ g.$ f (x) = -5x - 9 g (x) = x + 5

Use a graphing utility to graph the function and determine whether the function is even, odd, or neither. $f ( x ) = x ^ { 2 } - x ^ { 4 }$

Find ( f ? g )(x). $f ( x ) = \frac { 2 x } { 6 x + 9 }$ $g ( x ) = - \frac { 9 } { x }$

Given $y = \frac { x ^ { 3 } } { x ^ { 4 } + 1 }$ , use the algebraic tests to determine symmetry with respect to both axes and the origin.

Describe the sequence of transformations from $f ( x ) = | x |$ to $g$ . Then sketch the graph of $g$ by hand. Verify with a graphing utility. $f ( x ) = | x | + 2$

Determine the domain of $f \circ g$ if $f ( x ) = x ^ { 2 } - 17$ and $g ( x ) = \sqrt { x }.$

Sketch the graph of the function. $f ( x ) =$

Match the equation below with its graph. $y = 4 + x$ Graph I : Graph IV : Graph II : Graph V : Graph III :

Sketch the graph of the equation below. $y = \sqrt { x + 1 }$

Find the slope of the line that passes through the points $A ( - 4 , - 2 ) \text { and } B ( 10,9 ).$

Use the graphs of f and g to evaluate the function. $Use the graphs of f and g to evaluate the function. ( f \circ g ) ( 3 )$ $Use the graphs of f and g to evaluate the function. ( f \circ g ) ( 3 )$ $( f \circ g ) ( 3 )$