Question 1

A point is located six units to the left of the y-axis and seven units above the x-axis.Find the coordinates of the point. ​

Accepted Answer

A) (-6, 7) 
B) (7, 6) 
C) (-6, -7) 
D) (6, -7) 
E) (6, 7) 
A) (-6, 7) 
B) (7, 6) 
C) (-6, -7) 
D) (6, -7) 
E) (6, 7)

Question 2

Find the zeros of the function algebraically.
 $f ( x ) = \sqrt { 5 x + 2 }$

Accepted Answer

A)  $x = - \frac { 2 } { 5 }$ 
B)  $x = \frac { 2 } { 5 }$ 
C)   $x = \frac { 5 } { 2 }$ 
D)  $x = - \frac { 5 } { 2 }$ 
E)  $x = - 2$ 
A)  $x = - \frac { 2 } { 5 }$ 
B)  $x = \frac { 2 } { 5 }$ 
C)   $x = \frac { 5 } { 2 }$ 
D)  $x = - \frac { 5 } { 2 }$ 
E)  $x = - 2$

Question 3

Find the distance between the points. ​
(-8, -5), (-2, 3)
​

Accepted Answer

A) 10​ 
B) 100 
C) 2 
D) 5 
E) 8 
A) 10​ 
B) 100 
C) 2 
D) 5 
E) 8

Question 4

Use the graph of $f ( x ) = \sqrt { x }$ to write an equation for the function whose graph is shown.

Accepted Answer

A)   $y = \sqrt { x } + 5$ 
B)  $y = - \sqrt { x - 5 } + 5$ 
C)  $y = \sqrt { x + 5 } + 5$ 
D)  $y = - \sqrt { x } - 5$ 
E) None of the above 
A)   $y = \sqrt { x } + 5$ 
B)  $y = - \sqrt { x - 5 } + 5$ 
C)  $y = \sqrt { x + 5 } + 5$ 
D)  $y = - \sqrt { x } - 5$ 
E) None of the above

Question 5

Find the zeroes of the functions algebraically. 
 $f ( x ) = \sqrt { 5 x } - 9$

Accepted Answer

A)  $x = \pm \frac { 9 } { 5 }$ 
B)  $x = \pm \frac { 81 } { 5 }$ 
C)   $x = \frac { 9 } { 5 }$ 
D)   $x = \frac { 81 } { 5 }$ 
E)  no real zeroes 
A)  $x = \pm \frac { 9 } { 5 }$ 
B)  $x = \pm \frac { 81 } { 5 }$ 
C)   $x = \frac { 9 } { 5 }$ 
D)   $x = \frac { 81 } { 5 }$ 
E)  no real zeroes

Question 6

Find any x- or y-intercepts for the graph of the equation $y = x ^ { 2 } - 8 x + 12$ .

Accepted Answer

A) x-intercepts: (0, 12)y-intercepts: (2, 0), (6, 0) 
B) x-intercepts: (-2, 0), (-6, 0)y-intercepts: (0, 12) 
C) x-intercepts: (2, 0), (6, 0)y-intercepts: none 
D) x-intercepts: (0, 2), (0, 6)y-intercepts: (12, 0) 
E) x-intercepts: (2, 0), (6, 0)y-intercepts: (0, 12) 
A) x-intercepts: (0, 12)y-intercepts: (2, 0), (6, 0) 
B) x-intercepts: (-2, 0), (-6, 0)y-intercepts: (0, 12) 
C) x-intercepts: (2, 0), (6, 0)y-intercepts: none 
D) x-intercepts: (0, 2), (0, 6)y-intercepts: (12, 0) 
E) x-intercepts: (2, 0), (6, 0)y-intercepts: (0, 12)

Question 7

Find the x-intercept of the graph of the equation $y = 3 \sqrt { x - 6 }$ .

Accepted Answer

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

Question 8

Find $f \circ g$ and the domain of the composite function. 
 $f ( x ) = \frac { 1 } { x } , g ( x ) = x + 7$

Accepted Answer

A)  $\frac { 1 } { x } + 7$ Domain of $f \circ g$ : all real numbers x except $x = 0$ 
B)  $- \frac { 1 } { x + 7 }$ Domain of $f \circ g$ : all real numbers x except $x = - 7$ 
C)  $\frac { 1 } { x + 7 }$ Domain of $f \circ g$ : all real numbers x except $x = - 7$ 
D)  $\frac { 1 } { x } - 7$ Domain of $f \circ g$ : all real numbers x except $x = 0$ 
E)  $\frac { 1 } { x - 7 }$ Domain of $f \circ g$ : all real numbers x except $x = 7$ 
A)  $\frac { 1 } { x } + 7$ Domain of $f \circ g$ : all real numbers x except $x = 0$ 
B)  $- \frac { 1 } { x + 7 }$ Domain of $f \circ g$ : all real numbers x except $x = - 7$ 
C)  $\frac { 1 } { x + 7 }$ Domain of $f \circ g$ : all real numbers x except $x = - 7$ 
D)  $\frac { 1 } { x } - 7$ Domain of $f \circ g$ : all real numbers x except $x = 0$ 
E)  $\frac { 1 } { x - 7 }$ Domain of $f \circ g$ : all real numbers x except $x = 7$

Question 9

Find all real values of x such that f(x) = 0. ​
F(x) = x2 - 8x - 20
​

Accepted Answer

A) x = -10, 2 
B) x = -10, -2 
C) x = 2, 10 
D) x = -2, 10 
E) x = -8, 8 
A) x = -10, 2 
B) x = -10, -2 
C) x = 2, 10 
D) x = -2, 10 
E) x = -8, 8

Question 10

Evaluate the difference quotient for the function.  
F (x) = 2x - 7

Accepted Answer

A) -7 
B)  $\frac { 7 } { 2 }$ 
C) 7 
D) 2x + 7 
E) 2 
A) -7 
B)  $\frac { 7 } { 2 }$ 
C) 7 
D) 2x + 7 
E) 2

Question 11

Write an equation for the function that is described by the given characteristic.  
The shape of $f ( x ) = \sqrt { x }$ , but shifted three units to the left and reflected in both the x-axis and the y-axis.

Accepted Answer

A)  $g ( x ) = \sqrt { - x + 3 }$ 
B)  $g ( x ) = - \sqrt { x + 3 }$ 
C)  $g ( x ) = - \sqrt { - x + 3 }$ 
D)  $g ( x ) = \sqrt { x + 3 }$ 
E)  $g ( x ) = - \sqrt { - x - 3 }$ 
A)  $g ( x ) = \sqrt { - x + 3 }$ 
B)  $g ( x ) = - \sqrt { x + 3 }$ 
C)  $g ( x ) = - \sqrt { - x + 3 }$ 
D)  $g ( x ) = \sqrt { x + 3 }$ 
E)  $g ( x ) = - \sqrt { - x - 3 }$

Question 12

Select the correct graph of the given function.   $f ( x ) = 2.7 x - 5.5$

Accepted Answer

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

Question 13

The research and development department of an automobile manufacturer has determined that when a driver is required to stop quickly to avoid an accident, the distance (in feet) the car travels during the driver's reaction time is given by $R ( x ) = \frac { 5 } { 2 } x$ , where x is the speed of the car in miles per hour.The distance (in feet) traveled while the driver is braking is given by $B ( x ) = \frac { 1 } { 11 } x ^ { 2 }$ .Find the function that represents the total stopping distance T.

Accepted Answer

A)  $T = - \frac { 5 } { 2 } x + \frac { 1 } { 11 } x ^ { 2 }$ 
B)  $T = \frac { 5 } { 2 } x - \frac { 1 } { 11 } x ^ { 2 }$ 
C)  $T = \frac { 5 } { 2 } x ^ { 2 } + \frac { 1 } { 11 } x ^ { 2 }$ 
D)  $T = - \frac { 5 } { 2 } x - \frac { 1 } { 11 } x ^ { 2 }$ 
E)  $T = \frac { 5 } { 2 } x + \frac { 1 } { 11 } x ^ { 2 }$ 
A)  $T = - \frac { 5 } { 2 } x + \frac { 1 } { 11 } x ^ { 2 }$ 
B)  $T = \frac { 5 } { 2 } x - \frac { 1 } { 11 } x ^ { 2 }$ 
C)  $T = \frac { 5 } { 2 } x ^ { 2 } + \frac { 1 } { 11 } x ^ { 2 }$ 
D)  $T = - \frac { 5 } { 2 } x - \frac { 1 } { 11 } x ^ { 2 }$ 
E)  $T = \frac { 5 } { 2 } x + \frac { 1 } { 11 } x ^ { 2 }$

Question 14

Plot the point (-3, 1) on the Cartesian plane. ​

Accepted Answer

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

Question 15

Select the graph of the function, and use the Horizontal Line Test to determine whether the function is one-to-one and so has an inverse function.   $g ( x ) = \frac { 4 - x } { 5 }$

Accepted Answer

A)    The function has an inverse. 
B)    The function has an inverse. 
C)    The function has an inverse. 
D)    The function has an inverse. 
E)     The function has an inverse. 
A)    The function has an inverse. 
B)    The function has an inverse. 
C)    The function has an inverse. 
D)    The function has an inverse. 
E)     The function has an inverse.

Question 16

Find the zeros of the function algebraically. 
 $f ( x ) = \frac { 1 } { 8 } x ^ { 3 } - x$

Accepted Answer

A)  $x = 0 , \sqrt { 8 }$ 
B)  $x = 0 , - \sqrt { 8 }$ 
C)  $x = 0 , \pm 8$ 
D)  $x = 0 , \pm \sqrt { 8 }$ 
E)  $x = 0,8$ 
A)  $x = 0 , \sqrt { 8 }$ 
B)  $x = 0 , - \sqrt { 8 }$ 
C)  $x = 0 , \pm 8$ 
D)  $x = 0 , \pm \sqrt { 8 }$ 
E)  $x = 0,8$

Question 17

Find the distance between the two points (6, 1) and (6, 7).

Accepted Answer

A) 1 
B) 13 
C) 12 
D) 11 
E) 6 
A) 1 
B) 13 
C) 12 
D) 11 
E) 6

Question 18

Graphically estimate the x- and y-intercepts of the graph.
 $$y = x ^ { 3 } - x$$

Accepted Answer

A) x-intercept: (±1, 0), (0, 0)y-intercept: (0, 0) 
B) x-intercept: (1, 0), (0, 0)y-intercept: (0, 0) 
C) x-intercept: (-1, 0), (0, 0)y-intercept: (0, 0) 
D) x-intercept: (0, ±1), (0, 0)y-intercept: (0, 0) 
E) x-intercept: (0, 1), (0, 0) y-intercept: (0, 0) 
A) x-intercept: (±1, 0), (0, 0)y-intercept: (0, 0) 
B) x-intercept: (1, 0), (0, 0)y-intercept: (0, 0) 
C) x-intercept: (-1, 0), (0, 0)y-intercept: (0, 0) 
D) x-intercept: (0, ±1), (0, 0)y-intercept: (0, 0) 
E) x-intercept: (0, 1), (0, 0) y-intercept: (0, 0)

Question 19

Select the linear function such that it has the indicated function values. 
 $f ( 8 ) = 16 , f ( - 3 ) = - 17$

Accepted Answer

A)  $f ( x ) = 3 x - 8$ 
B)  $f ( x ) = - 3 x + 3$ 
C)  $f ( x ) = 3 x + 8$ 
D)  $f ( x ) = 8 x + 3$ 
E)  $f ( x ) = - 3 x - 3$ 
A)  $f ( x ) = 3 x - 8$ 
B)  $f ( x ) = - 3 x + 3$ 
C)  $f ( x ) = 3 x + 8$ 
D)  $f ( x ) = 8 x + 3$ 
E)  $f ( x ) = - 3 x - 3$

Question 20

Select the graph of the function. 
 $f ( x ) = \left\{ \begin{array} { c c } 
5 - x ^ { 2 } & x < - 2 \
3 + x & - 2 \leq x < 0 \
x ^ { 2 } + 3 & x \geq 0
\end{array} \right.$

Accepted Answer

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

A point is located six units to the left of the y-axis and seven units above the x-axis.Find the coordinates of the point.

Find the zeros of the function algebraically. $f ( x ) = \sqrt { 5 x + 2 }$

Find the distance between the points. (-8, -5), (-2, 3)

Use the graph of $f ( x ) = \sqrt { x }$ to write an equation for the function whose graph is shown. $Use the graph of f ( x ) = \sqrt { x } to write an equation for the function whose graph is shown.$

Find the zeroes of the functions algebraically. $f ( x ) = \sqrt { 5 x } - 9$

Find any x- or y-intercepts for the graph of the equation $y = x ^ { 2 } - 8 x + 12$ .

Find the x-intercept of the graph of the equation $y = 3 \sqrt { x - 6 }$ .

Find $f \circ g$ and the domain of the composite function. $f ( x ) = \frac { 1 } { x } , g ( x ) = x + 7$

Find all real values of x such that f(x) = 0. F(x) = x² - 8x - 20

Evaluate the difference quotient for the function. F (x) = 2x - 7

Write an equation for the function that is described by the given characteristic. The shape of $f ( x ) = \sqrt { x }$ , but shifted three units to the left and reflected in both the x-axis and the y-axis.

Select the correct graph of the given function. $f ( x ) = 2.7 x - 5.5$

Plot the point (-3, 1) on the Cartesian plane.

Select the graph of the function, and use the Horizontal Line Test to determine whether the function is one-to-one and so has an inverse function. $g ( x ) = \frac { 4 - x } { 5 }$

Find the zeros of the function algebraically. $f ( x ) = \frac { 1 } { 8 } x ^ { 3 } - x$

Find the distance between the two points (6, 1) and (6, 7).

Graphically estimate the x- and y-intercepts of the graph. $y = x ^ { 3 } - x$ $Graphically estimate the x- and y-intercepts of the graph. y = x ^ { 3 } - x$

Select the linear function such that it has the indicated function values. $f ( 8 ) = 16 , f ( - 3 ) = - 17$

Select the graph of the function. $f ( x ) = \left\{ \begin{array} { c c } 5 - x ^ { 2 } & x < - 2 \\3 + x & - 2 \leq x < 0 \\x ^ { 2 } + 3 & x \geq 0\end{array} \right.$

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

Exam 1: Functions and Their Graphs

A point is located six units to the left of the y-axis and seven units above the x-axis.Find the coordinates of the point. ​

Find the zeros of the function algebraically. f(x)=5x+2f ( x ) = \sqrt { 5 x + 2 }f(x)=5x+2​

Find the distance between the points. ​ (-8, -5), (-2, 3) ​

Use the graph of f(x)=xf ( x ) = \sqrt { x }f(x)=x​ to write an equation for the function whose graph is shown.

Find the zeroes of the functions algebraically. f(x)=5x−9f ( x ) = \sqrt { 5 x } - 9f(x)=5x​−9

Find any x- or y-intercepts for the graph of the equation y=x2−8x+12y = x ^ { 2 } - 8 x + 12y=x2−8x+12 .

Find the x-intercept of the graph of the equation y=3x−6y = 3 \sqrt { x - 6 }y=3x−6​ .

Find f∘gf \circ gf∘g and the domain of the composite function. f(x)=1x,g(x)=x+7f ( x ) = \frac { 1 } { x } , g ( x ) = x + 7f(x)=x1​,g(x)=x+7

Find all real values of x such that f(x) = 0. ​ F(x) = x2 - 8x - 20 ​

Evaluate the difference quotient for the function. F (x) = 2x - 7

Write an equation for the function that is described by the given characteristic. The shape of f(x)=xf ( x ) = \sqrt { x }f(x)=x​ , but shifted three units to the left and reflected in both the x-axis and the y-axis.

Select the correct graph of the given function. f(x)=2.7x−5.5f ( x ) = 2.7 x - 5.5f(x)=2.7x−5.5

Plot the point (-3, 1) on the Cartesian plane. ​

Select the graph of the function, and use the Horizontal Line Test to determine whether the function is one-to-one and so has an inverse function. g(x)=4−x5g ( x ) = \frac { 4 - x } { 5 }g(x)=54−x​

Find the zeros of the function algebraically. f(x)=18x3−xf ( x ) = \frac { 1 } { 8 } x ^ { 3 } - xf(x)=81​x3−x

Find the distance between the two points (6, 1) and (6, 7).

Graphically estimate the x- and y-intercepts of the graph. y=x3−xy = x ^ { 3 } - xy=x3−x

Select the linear function such that it has the indicated function values. f(8)=16,f(−3)=−17f ( 8 ) = 16 , f ( - 3 ) = - 17f(8)=16,f(−3)=−17

Select the graph of the function. f(x)={5−x2x<−23+x−2≤x<0x2+3x≥0f ( x ) = \left\{ \begin{array} { c c } 5 - x ^ { 2 } & x < - 2 \\3 + x & - 2 \leq x < 0 \\x ^ { 2 } + 3 & x \geq 0\end{array} \right.f(x)=⎩⎨⎧​5−x23+xx2+3​x<−2−2≤x<0x≥0​

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

A point is located six units to the left of the y-axis and seven units above the x-axis.Find the coordinates of the point.

Find the zeros of the function algebraically. $f ( x ) = \sqrt { 5 x + 2 }$

Find the distance between the points. (-8, -5), (-2, 3)

Use the graph of $f ( x ) = \sqrt { x }$ to write an equation for the function whose graph is shown. $Use the graph of f ( x ) = \sqrt { x } to write an equation for the function whose graph is shown.$

Find the zeroes of the functions algebraically. $f ( x ) = \sqrt { 5 x } - 9$

Find any x- or y-intercepts for the graph of the equation $y = x ^ { 2 } - 8 x + 12$ .

Find the x-intercept of the graph of the equation $y = 3 \sqrt { x - 6 }$ .

Find $f \circ g$ and the domain of the composite function. $f ( x ) = \frac { 1 } { x } , g ( x ) = x + 7$

Find all real values of x such that f(x) = 0. F(x) = x² - 8x - 20

Write an equation for the function that is described by the given characteristic. The shape of $f ( x ) = \sqrt { x }$ , but shifted three units to the left and reflected in both the x-axis and the y-axis.

Select the correct graph of the given function. $f ( x ) = 2.7 x - 5.5$

Plot the point (-3, 1) on the Cartesian plane.

Select the graph of the function, and use the Horizontal Line Test to determine whether the function is one-to-one and so has an inverse function. $g ( x ) = \frac { 4 - x } { 5 }$

Find the zeros of the function algebraically. $f ( x ) = \frac { 1 } { 8 } x ^ { 3 } - x$

Graphically estimate the x- and y-intercepts of the graph. $y = x ^ { 3 } - x$ $Graphically estimate the x- and y-intercepts of the graph. y = x ^ { 3 } - x$

Select the linear function such that it has the indicated function values. $f ( 8 ) = 16 , f ( - 3 ) = - 17$

Select the graph of the function. $f ( x ) = \left\{ \begin{array} { c c } 5 - x ^ { 2 } & x < - 2 \\3 + x & - 2 \leq x < 0 \\x ^ { 2 } + 3 & x \geq 0\end{array} \right.$