Question 1

Show that the points form the vertices of the indicated polygon.  
Right triangle: (3, 5), (5, 6), (6, 4)

Accepted Answer

A)  $( \sqrt { 5 } ) ^ { 2 } + ( \sqrt { 5 } ) ^ { 2 } = ( \sqrt { 10 } ) ^ { 2 }$ 
B)  $( \sqrt { 31 } ) ^ { 2 } + ( \sqrt { 5 } ) ^ { 2 } = ( \sqrt { 10 } ) ^ { 2 }$ 
C)  $( \sqrt { 7 } ) ^ { 2 } + ( \sqrt { 5 } ) ^ { 2 } = ( \sqrt { 10 } ) ^ { 2 }$ 
D)  $( \sqrt { 11 } ) ^ { 2 } + ( \sqrt { 5 } ) ^ { 2 } = ( \sqrt { 10 } ) ^ { 2 }$ 
E)  $( \sqrt { 34 } ) ^ { 2 } + ( \sqrt { 5 } ) ^ { 2 } = ( \sqrt { 10 } ) ^ { 2 }$ 
A)  $( \sqrt { 5 } ) ^ { 2 } + ( \sqrt { 5 } ) ^ { 2 } = ( \sqrt { 10 } ) ^ { 2 }$ 
B)  $( \sqrt { 31 } ) ^ { 2 } + ( \sqrt { 5 } ) ^ { 2 } = ( \sqrt { 10 } ) ^ { 2 }$ 
C)  $( \sqrt { 7 } ) ^ { 2 } + ( \sqrt { 5 } ) ^ { 2 } = ( \sqrt { 10 } ) ^ { 2 }$ 
D)  $( \sqrt { 11 } ) ^ { 2 } + ( \sqrt { 5 } ) ^ { 2 } = ( \sqrt { 10 } ) ^ { 2 }$ 
E)  $( \sqrt { 34 } ) ^ { 2 } + ( \sqrt { 5 } ) ^ { 2 } = ( \sqrt { 10 } ) ^ { 2 }$

Question 2

If f(x) = x + 1 and g(x) = 5x, then $( f \circ g ) ( x ) = ( g \circ f ) ( x )$ .

Accepted Answer

A) True 
 B)False

Question 3

Write the standard form of the equation of the circle with the given characteristics. endpoints of a diameter: (3, 4), (7, 8)

Accepted Answer

A)  $( x - 5 ) ^ { 2 } + ( y - 6 ) ^ { 2 } = 8$ 
B)  $( x - 6 ) ^ { 2 } + ( y - 5 ) ^ { 2 } = 8$ 
C)  $( x + 5 ) ^ { 2 } + ( y + 6 ) ^ { 2 } = 8$ 
D)  $( x + 5 ) ^ { 2 } + ( y - 6 ) ^ { 2 } = 340$ 
E)  $( x - 5 ) ^ { 2 } + ( y + 6 ) ^ { 2 } = 340$ 
A)  $( x - 5 ) ^ { 2 } + ( y - 6 ) ^ { 2 } = 8$ 
B)  $( x - 6 ) ^ { 2 } + ( y - 5 ) ^ { 2 } = 8$ 
C)  $( x + 5 ) ^ { 2 } + ( y + 6 ) ^ { 2 } = 8$ 
D)  $( x + 5 ) ^ { 2 } + ( y - 6 ) ^ { 2 } = 340$ 
E)  $( x - 5 ) ^ { 2 } + ( y + 6 ) ^ { 2 } = 340$

Question 4

Show that the points form the vertices of the indicated polygon.  
Isosceles triangle: (7, -6), (9, 8), (-5, 6)

Accepted Answer

A) Distances between the points: $\sqrt { 37 } , \sqrt { 200 } , \sqrt { 288 }$ 
B) Distances between the points: $\sqrt { 200 } , \sqrt { 200 } , \sqrt { 288 }$ 
C) Distances between the points: $\sqrt { 26 } , \sqrt { 200 } , \sqrt { 288 }$ 
D) Distances between the points: $\sqrt { 43 } , \sqrt { 200 } , \sqrt { 288 }$ 
E) Distances between the points: $\sqrt { 19 } , \sqrt { 200 } , \sqrt { 288 }$ 
A) Distances between the points: $\sqrt { 37 } , \sqrt { 200 } , \sqrt { 288 }$ 
B) Distances between the points: $\sqrt { 200 } , \sqrt { 200 } , \sqrt { 288 }$ 
C) Distances between the points: $\sqrt { 26 } , \sqrt { 200 } , \sqrt { 288 }$ 
D) Distances between the points: $\sqrt { 43 } , \sqrt { 200 } , \sqrt { 288 }$ 
E) Distances between the points: $\sqrt { 19 } , \sqrt { 200 } , \sqrt { 288 }$

Question 5

Find the slope of the line passing through the pair of points. ​
P(-4, 3); Q(2, -9).
​

Accepted Answer

A) m = 1 
B) m = -7 
C) m = 4 
D) m = -2 
E) m = -1 
A) m = 1 
B) m = -7 
C) m = 4 
D) m = -2 
E) m = -1

Question 6

Find the midpoint of the line segment joining the points (3, 6) and (9, -4). ​

Accepted Answer

A) (6, -10) 
B) (12, 2) 
C) (6, 1) 
D) (-3, 5) 
E) (3, -5) 
A) (6, -10) 
B) (12, 2) 
C) (6, 1) 
D) (-3, 5) 
E) (3, -5)

Question 7

Find the y-intercept of the graph of the equation y = 3x + 18. ​

Accepted Answer

A) (0, 3) 
B) (18, 0) 
C) (-6, 0) 
D) (0, 18) 
E) (0, -6) 
A) (0, 3) 
B) (18, 0) 
C) (-6, 0) 
D) (0, 18) 
E) (0, -6)

Question 8

The coiled spring of a toy supports the weight of a child.The spring is compressed a distance of 1.6 inches by the weight of a 35-pound child.The toy will not work properly if its spring is compressed more than 6 inches.What is the weight of the heaviest child who should be allowed to use the toy? (Round your answer to two decimal places.) ?

Accepted Answer

A) 136.25 lb 
B) 126.25 lb 
C) 131.25 lb 
D) 35 lb 
E) 141.25 lb 
A) 136.25 lb 
B) 126.25 lb 
C) 131.25 lb 
D) 35 lb 
E) 141.25 lb

Question 9

The total numbers of Navy personnel N (in thousands) and Marines personnel M (in thousands) from 2000 through 2007 can be approximated by the models 
 $N ( t ) = 0.194 t ^ { 3 } - 7.88 t ^ { 2 } + 12.9 t + 375$ and $M ( t ) = 0.031 t ^ { 3 } - 0.25 t ^ { 2 } + 6.7 t + 173$  
Where t represents the year, with t = 0 corresponding to 2000.
Find and interpret $( N - M ) ( t )$ .

Accepted Answer

A)  $( N - M ) ( t ) = 0.163 t ^ { 3 } + 7.63 t ^ { 2 } - 6.2 t + 202$ , which represents the difference between the number of Navy personnel and the number of Marines personnel. 
B)  $( N - M ) ( t ) = 0.163 t ^ { 3 } - 7.63 t ^ { 2 } - 6.2 t - 202$ , which represents the difference between the number of Navy personnel and the number of Marines personnel. 
C)  $( N - M ) ( t ) = 0.163 t ^ { 3 } - 7.63 t ^ { 2 } - 6.2 t + 202$ , which represents the difference between the number of Navy personnel and the number of Marines personnel. 
D)  $( N - M ) ( t ) = 0.163 t ^ { 3 } + 7.63 t ^ { 2 } + 6.2 t + 202$ , which represents the difference between the number of Navy personnel and the number of Marines personnel. 
E)  $( N - M ) ( t ) = 0.163 t ^ { 3 } - 7.63 t ^ { 2 } + 6.2 t + 202$ , which represents the difference between the number of Navy personnel and the number of Marines personnel. 
A)  $( N - M ) ( t ) = 0.163 t ^ { 3 } + 7.63 t ^ { 2 } - 6.2 t + 202$ , which represents the difference between the number of Navy personnel and the number of Marines personnel. 
B)  $( N - M ) ( t ) = 0.163 t ^ { 3 } - 7.63 t ^ { 2 } - 6.2 t - 202$ , which represents the difference between the number of Navy personnel and the number of Marines personnel. 
C)  $( N - M ) ( t ) = 0.163 t ^ { 3 } - 7.63 t ^ { 2 } - 6.2 t + 202$ , which represents the difference between the number of Navy personnel and the number of Marines personnel. 
D)  $( N - M ) ( t ) = 0.163 t ^ { 3 } + 7.63 t ^ { 2 } + 6.2 t + 202$ , which represents the difference between the number of Navy personnel and the number of Marines personnel. 
E)  $( N - M ) ( t ) = 0.163 t ^ { 3 } - 7.63 t ^ { 2 } + 6.2 t + 202$ , which represents the difference between the number of Navy personnel and the number of Marines personnel.

Question 10

Select the graph of the function and find the zeros of the function. 
 $f ( x ) = x ( x - 6 )$

Accepted Answer

A)       x = 0, 9 
B)      x = -6, 0 
C)      x = -6, 0 
D)     x = 6 
E)    x = 0, 6 
A)       x = 0, 9 
B)      x = -6, 0 
C)      x = -6, 0 
D)     x = 6 
E)    x = 0, 6

Question 11

Evaluate the indicated function for $f ( x ) = x ^ { 2 } + 5$ and $g ( x ) = x - 4$ .   $( f / g ) ( 5 )$

Accepted Answer

A) 30 
B)  $\frac { 5 } { 34 }$ 
C)  $\frac { 32 } { 3 }$ 
D)  $\frac { 2 } { 31 }$ 
E)  $\frac { 34 } { 5 }$ 
A) 30 
B)  $\frac { 5 } { 34 }$ 
C)  $\frac { 32 } { 3 }$ 
D)  $\frac { 2 } { 31 }$ 
E)  $\frac { 34 } { 5 }$

Question 12

Find all real value of x such that f (x) = 0. f(x) = 64x2 - 36

Accepted Answer

A)  x = ± $\frac { 4 } { 3 }$ 
B)  x = ± $\frac { 3 } { 4 }$ 
C)  x = - $\frac { 9 } { 16 }$ 
D)  x = $\frac { 4 } { 3 }$ 
E)  x = ± $\frac { 9 } { 16 }$ 
A)  x = ± $\frac { 4 } { 3 }$ 
B)  x = ± $\frac { 3 } { 4 }$ 
C)  x = - $\frac { 9 } { 16 }$ 
D)  x = $\frac { 4 } { 3 }$ 
E)  x = ± $\frac { 9 } { 16 }$

Question 13

Use the functions given by f(x) = x + 6 and g(x) = 7x - 3 to find g-1 º f-1.

Accepted Answer

A)  $\frac { - x - 3 } { 7 }$ 
B)  $\frac { x + 3 } { 7 }$ 
C)  $\frac { x - 3 } { 7 }$ 
D)  $\frac { x - 3 } { - 7 }$ 
E)  $\frac { x - 7 } { 3 }$ 
A)  $\frac { - x - 3 } { 7 }$ 
B)  $\frac { x + 3 } { 7 }$ 
C)  $\frac { x - 3 } { 7 }$ 
D)  $\frac { x - 3 } { - 7 }$ 
E)  $\frac { x - 7 } { 3 }$

Question 14

Find the slope-intercept form of the equation of the line that passes through the given point and has the indicated slope m.Select correct answer for the line.   $\mathrm { P } ( 0,0 ) , m = 2$

Accepted Answer

A)  $y = 2 x - 2$   
B)  $y = 2 x + 2$   
C)  $y = - 2 x$   
D)  $y = - 2 x - 2$   
E)  $y = 2 x$   
A)  $y = 2 x - 2$   
B)  $y = 2 x + 2$   
C)  $y = - 2 x$   
D)  $y = - 2 x - 2$   
E)  $y = 2 x$

Question 15

Evaluate the indicated function for $f ( x ) = x ^ { 2 } - 6$ and $g ( x ) = x + 4$ . ( fg )(1)

Accepted Answer

A) 15 
B) -35 
C) -23 
D) -25 
E) -33 
A) 15 
B) -35 
C) -23 
D) -25 
E) -33

Question 16

Let the function f be defined by the equation y = f (x) , where x and f (x) are real numbers.Find the domain and range of the function $f ( x ) = \sqrt { 25 x ^ { 2 } - 3 }$ .

Accepted Answer

A) domain: $\left( - \infty , - \frac { 3 } { 25 } \right)$ 
B) domain: $\left( - \frac { 3 } { 5 } , \frac { 3 } { 5 } \right)$ 
C) domain: $\left( - \infty , - \frac { 3 } { 25 } \right] \cup \left[ \frac { 3 } { 25 } , + \infty \right)$ 
D) domain: $\left( \frac { \sqrt { 3 } } { 5 } , + \infty \right)$ 
E) domain: $\left( - \infty , - \frac { \sqrt { 3 } } { 5 } \right] \cup \left[ \frac { \sqrt { 3 } } { 5 } , + \infty \right)$ 
A) domain: $\left( - \infty , - \frac { 3 } { 25 } \right)$ 
B) domain: $\left( - \frac { 3 } { 5 } , \frac { 3 } { 5 } \right)$ 
C) domain: $\left( - \infty , - \frac { 3 } { 25 } \right] \cup \left[ \frac { 3 } { 25 } , + \infty \right)$ 
D) domain: $\left( \frac { \sqrt { 3 } } { 5 } , + \infty \right)$ 
E) domain: $\left( - \infty , - \frac { \sqrt { 3 } } { 5 } \right] \cup \left[ \frac { \sqrt { 3 } } { 5 } , + \infty \right)$

Question 17

Find the domain of the function. $f ( w ) = \frac { 8 w } { w + 6 }$

Accepted Answer

A) w = -6, w = 0 
B) w = -6 
C) all real numbers w $\neq$ -6, w $\neq$ 0 
D) all real numbers 
E) all real numbers w $\neq$ -6 
A) w = -6, w = 0 
B) w = -6 
C) all real numbers w $\neq$ -6, w $\neq$ 0 
D) all real numbers 
E) all real numbers w $\neq$ -6

Question 18

Find $g \circ f$ . 
$f ( x ) = x ^ { 2 } , g ( x ) = x - 4$

Accepted Answer

A)  $x ^ { 2 } - 4$ 
B)  $x ^ { 2 }$ 
C)  $( x - 4 ) ^ { 2 }$ 
D)  $\left( x ^ { 2 } + 4 \right)$ 
E)  $( x + 4 ) ^ { 2 }$ 
A)  $x ^ { 2 } - 4$ 
B)  $x ^ { 2 }$ 
C)  $( x - 4 ) ^ { 2 }$ 
D)  $\left( x ^ { 2 } + 4 \right)$ 
E)  $( x + 4 ) ^ { 2 }$

Question 19

An object is thrown upward from ground level at a velocity of 90 feet per second. Use the position equation s = -16t2 + v0t + s0 to select a function that represents the situation and select the graph of the function.
​

Accepted Answer

A) s = -16t2 + 90t​​   
B) s = -16t2 - 90t​   
C) s = 16t2 + 90t​​   
D) s = 16t2 - 90t​​   
E) s = -16t2 + 90t + 8​​   
A) s = -16t2 + 90t​​   
B) s = -16t2 - 90t​   
C) s = 16t2 + 90t​​   
D) s = 16t2 - 90t​​   
E) s = -16t2 + 90t + 8​​

Question 20

Graph the circle $( x - 2 ) ^ { 2 } + ( y - 8 ) ^ { 2 } = 25$ .

Accepted Answer

A)    
B)     
C)     
D)    
E) None of the above. 
A)    
B)     
C)     
D)    
E) None of the above.

Show that the points form the vertices of the indicated polygon. Right triangle: (3, 5), (5, 6), (6, 4)

If f(x) = x + 1 and g(x) = 5x, then $( f \circ g ) ( x ) = ( g \circ f ) ( x )$ .

Write the standard form of the equation of the circle with the given characteristics. endpoints of a diameter: (3, 4), (7, 8)

Show that the points form the vertices of the indicated polygon. Isosceles triangle: (7, -6), (9, 8), (-5, 6)

Find the slope of the line passing through the pair of points. P(-4, 3); Q(2, -9).

Find the midpoint of the line segment joining the points (3, 6) and (9, -4).

Find the y-intercept of the graph of the equation y = 3x + 18.

Select the graph of the function and find the zeros of the function. $f ( x ) = x ( x - 6 )$

Evaluate the indicated function for $f ( x ) = x ^ { 2 } + 5$ and $g ( x ) = x - 4$ . $( f / g ) ( 5 )$

Find all real value of x such that f (x) = 0. f(x) = 64x² - 36

Use the functions given by f(x) = x + 6 and g(x) = 7x - 3 to find g^-1 _º f^-1.

Find the slope-intercept form of the equation of the line that passes through the given point and has the indicated slope m.Select correct answer for the line. $\mathrm { P } ( 0,0 ) , m = 2$

Evaluate the indicated function for $f ( x ) = x ^ { 2 } - 6$ and $g ( x ) = x + 4$ . ( fg )(1)

Let the function f be defined by the equation y = f (x) , where x and f (x) are real numbers.Find the domain and range of the function $f ( x ) = \sqrt { 25 x ^ { 2 } - 3 }$ .

Find the domain of the function. $f ( w ) = \frac { 8 w } { w + 6 }$

Find $g \circ f$ . $f ( x ) = x ^ { 2 } , g ( x ) = x - 4$

An object is thrown upward from ground level at a velocity of 90 feet per second. Use the position equation s = -16t² + v₀t + s₀ to select a function that represents the situation and select the graph of the function.

Graph the circle $( x - 2 ) ^ { 2 } + ( y - 8 ) ^ { 2 } = 25$ .

Polynomial and Rational Functions

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

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Exam 1: Functions and Their Graphs

Show that the points form the vertices of the indicated polygon. Right triangle: (3, 5), (5, 6), (6, 4)

If f(x) = x + 1 and g(x) = 5x, then (f∘g)(x)=(g∘f)(x)( f \circ g ) ( x ) = ( g \circ f ) ( x )(f∘g)(x)=(g∘f)(x) .

Write the standard form of the equation of the circle with the given characteristics. endpoints of a diameter: (3, 4), (7, 8)

Show that the points form the vertices of the indicated polygon. Isosceles triangle: (7, -6), (9, 8), (-5, 6)

Find the slope of the line passing through the pair of points. ​ P(-4, 3); Q(2, -9). ​

Find the midpoint of the line segment joining the points (3, 6) and (9, -4). ​

Find the y-intercept of the graph of the equation y = 3x + 18. ​

Select the graph of the function and find the zeros of the function. f(x)=x(x−6)f ( x ) = x ( x - 6 )f(x)=x(x−6)

Evaluate the indicated function for f(x)=x2+5f ( x ) = x ^ { 2 } + 5f(x)=x2+5 and g(x)=x−4g ( x ) = x - 4g(x)=x−4 . (f/g)(5)( f / g ) ( 5 )(f/g)(5)

Find all real value of x such that f (x) = 0. f(x) = 64x2 - 36

Use the functions given by f(x) = x + 6 and g(x) = 7x - 3 to find g-1 º f-1.

Find the slope-intercept form of the equation of the line that passes through the given point and has the indicated slope m.Select correct answer for the line. P(0,0),m=2\mathrm { P } ( 0,0 ) , m = 2P(0,0),m=2

Evaluate the indicated function for f(x)=x2−6f ( x ) = x ^ { 2 } - 6f(x)=x2−6 and g(x)=x+4g ( x ) = x + 4g(x)=x+4 . ( fg )(1)

Let the function f be defined by the equation y = f (x) , where x and f (x) are real numbers.Find the domain and range of the function f(x)=25x2−3f ( x ) = \sqrt { 25 x ^ { 2 } - 3 }f(x)=25x2−3​ .

Find the domain of the function. f(w)=8ww+6f ( w ) = \frac { 8 w } { w + 6 }f(w)=w+68w​

Find g∘fg \circ fg∘f . f(x)=x2,g(x)=x−4f ( x ) = x ^ { 2 } , g ( x ) = x - 4f(x)=x2,g(x)=x−4

An object is thrown upward from ground level at a velocity of 90 feet per second. Use the position equation s = -16t2 + v0t + s0 to select a function that represents the situation and select the graph of the function. ​

Graph the circle (x−2)2+(y−8)2=25( x - 2 ) ^ { 2 } + ( y - 8 ) ^ { 2 } = 25(x−2)2+(y−8)2=25 .

Polynomial and Rational Functions

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

If f(x) = x + 1 and g(x) = 5x, then $( f \circ g ) ( x ) = ( g \circ f ) ( x )$ .

Find the slope of the line passing through the pair of points. P(-4, 3); Q(2, -9).

Find the midpoint of the line segment joining the points (3, 6) and (9, -4).

Find the y-intercept of the graph of the equation y = 3x + 18.

Select the graph of the function and find the zeros of the function. $f ( x ) = x ( x - 6 )$

Evaluate the indicated function for $f ( x ) = x ^ { 2 } + 5$ and $g ( x ) = x - 4$ . $( f / g ) ( 5 )$

Find all real value of x such that f (x) = 0. f(x) = 64x² - 36

Use the functions given by f(x) = x + 6 and g(x) = 7x - 3 to find g^-1 _º f^-1.

Find the slope-intercept form of the equation of the line that passes through the given point and has the indicated slope m.Select correct answer for the line. $\mathrm { P } ( 0,0 ) , m = 2$

Evaluate the indicated function for $f ( x ) = x ^ { 2 } - 6$ and $g ( x ) = x + 4$ . ( fg )(1)

Let the function f be defined by the equation y = f (x) , where x and f (x) are real numbers.Find the domain and range of the function $f ( x ) = \sqrt { 25 x ^ { 2 } - 3 }$ .

Find the domain of the function. $f ( w ) = \frac { 8 w } { w + 6 }$

Find $g \circ f$ . $f ( x ) = x ^ { 2 } , g ( x ) = x - 4$

An object is thrown upward from ground level at a velocity of 90 feet per second. Use the position equation s = -16t² + v₀t + s₀ to select a function that represents the situation and select the graph of the function.

Graph the circle $( x - 2 ) ^ { 2 } + ( y - 8 ) ^ { 2 } = 25$ .