Question 1

Find the slope of the line passing through the pair of points.  
P (-9, 14); Q (-18, -2)

Accepted Answer

A) m = $\frac { 16 } { 9 }$ 
B) m = - $\frac { 9 } { 16 }$ 
C) m = - $\frac { 16 } { 9 }$ 
D) m = $\frac { 9 } { 16 }$ 
E) none of these 
A) m = $\frac { 16 } { 9 }$ 
B) m = - $\frac { 9 } { 16 }$ 
C) m = - $\frac { 16 } { 9 }$ 
D) m = $\frac { 9 } { 16 }$ 
E) none of these

Question 2

Determine whether the function is one-to-one. ​
Y = (x - 5)2; x ≥ 5
​

Accepted Answer

A) No, it isn't one-to-one. 
B) Yes, it is one-to-one. 
A) No, it isn't one-to-one. 
B) Yes, it is one-to-one.

Question 3

Identify any intercepts and test for symmetry.Then sketch the graph of the equation.
 $y = x ^ { 3 } - 6$

Accepted Answer

A) x- intercept: ( $\sqrt [ 3 ] { 6 }$ , 0)y- intercept: (0, ±6)No symmetry   
B) x- intercept: ( $\sqrt [ 3 ] { 6 }$ , 0)y- intercept: (0, -6)No symmetry    
C) x- intercept: ( $\sqrt [ 3 ] { 6 }$ , 0)y- intercept: (0, 6)No symmetry   
D) x- intercept: ( $\sqrt [ 3 ] { - 6 }$ , 0)y- intercept: (0, 6)No symmetry    
E) x- intercept: ( $\sqrt [ 3 ] { - 6 }$ , 0)y- intercept: (0, ±6)No symmetry   
A) x- intercept: ( $\sqrt [ 3 ] { 6 }$ , 0)y- intercept: (0, ±6)No symmetry   
B) x- intercept: ( $\sqrt [ 3 ] { 6 }$ , 0)y- intercept: (0, -6)No symmetry    
C) x- intercept: ( $\sqrt [ 3 ] { 6 }$ , 0)y- intercept: (0, 6)No symmetry   
D) x- intercept: ( $\sqrt [ 3 ] { - 6 }$ , 0)y- intercept: (0, 6)No symmetry    
E) x- intercept: ( $\sqrt [ 3 ] { - 6 }$ , 0)y- intercept: (0, ±6)No symmetry

Question 4

Evaluate the function f(x) = [[3x + 1]] for x = 4. ​

Accepted Answer

A) f(x) = -4 
B) ​ f(x) = 4 
C) ​ f(x) = 11 
D) ​ f(x) = 13 
E) ​ f(x) = 12 
A) f(x) = -4 
B) ​ f(x) = 4 
C) ​ f(x) = 11 
D) ​ f(x) = 13 
E) ​ f(x) = 12

Question 5

Find the average rate of change of the function from x1 = 0 to x2 = 3. 
 $f ( x ) = 3 x + 10$

Accepted Answer

A) The average rate of change from x1 = 0 to x2 = 3 is -3. 
B) The average rate of change from x1 = 0 to x2 = 3 is 3. 
C) The average rate of change from x1 = 0 to x2 = 3 is -10. 
D) The average rate of change from  x1 = 0 to x2 = 3 is 10. 
E) The average rate of change from x1 = 0 to x2 = 3 is 19. 
A) The average rate of change from x1 = 0 to x2 = 3 is -3. 
B) The average rate of change from x1 = 0 to x2 = 3 is 3. 
C) The average rate of change from x1 = 0 to x2 = 3 is -10. 
D) The average rate of change from  x1 = 0 to x2 = 3 is 10. 
E) The average rate of change from x1 = 0 to x2 = 3 is 19.

Question 6

Which function does the graph represent

Accepted Answer

A)  g(x) = [[3x]] 
B)  g(x) = [[x+3]] 
C)  g(x) = 3[[x]] 
D)  g(x) = [[-4x]] 
E)  g(x) = [[x-3]] 
A)  g(x) = [[3x]] 
B)  g(x) = [[x+3]] 
C)  g(x) = 3[[x]] 
D)  g(x) = [[-4x]] 
E)  g(x) = [[x-3]]

Question 7

Select the correct graph, showing f and g are inverse functions. 
 $f ( x ) = \sqrt { x - 3 } , g ( x ) = x ^ { 2 } + 3 , x \geq 0$

Accepted Answer

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

Question 8

Let S represent the midpoint between (5, 3) and (-5, -7).Let T represent the midpoint between (5, 3) and S.Find the coordinates of T. ​

Accepted Answer

A) (-2.5, -4.5) 
B) (0, -2) 
C) (0, 0.5) 
D) (2.5, 0.5) 
E) (2.5, -2) 
A) (-2.5, -4.5) 
B) (0, -2) 
C) (0, 0.5) 
D) (2.5, 0.5) 
E) (2.5, -2)

Question 9

Select the graph of the function and determine whether it is even, odd, or neither. 
 $f ( x ) = \sqrt { 3 - x }$

Accepted Answer

A)    Even 
B)     Odd 
C)     Odd 
D)    Even 
E)    Neither 
A)    Even 
B)     Odd 
C)     Odd 
D)    Even 
E)    Neither

Question 10

Graphically estimate the x- and y-intercepts of the graph.
 $$y = 81 - 9 x ^ { 2 }$$

Accepted Answer

A) x-intercept: (±3, 0)y-intercept: (0, 81) 
B) x-intercept: (3, 0)y-intercept: (0, 81) 
C) x-intercept: (-3, 0)y-intercept: (0, 81) 
D) x-intercept: (±3, 0)y-intercept: (0, 9) 
E) x-intercept: (0, 3)y-intercept: (0, 81) 
A) x-intercept: (±3, 0)y-intercept: (0, 81) 
B) x-intercept: (3, 0)y-intercept: (0, 81) 
C) x-intercept: (-3, 0)y-intercept: (0, 81) 
D) x-intercept: (±3, 0)y-intercept: (0, 9) 
E) x-intercept: (0, 3)y-intercept: (0, 81)

Question 11

Find (f - g)(x).   $f ( x ) = x + 3 , g ( x ) = x - 3$

Accepted Answer

A) 2x - 6 
B) 6 
C) 2x - 3 
D) 2x + 6 
E) 2x 
A) 2x - 6 
B) 6 
C) 2x - 3 
D) 2x + 6 
E) 2x

Question 12

Use the graph of $f ( x ) = x ^ { 2 }$ to write an equation for the function whose graph is shown.

Accepted Answer

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

Question 13

Use the given graph of f to select the graph for following function. 
 $y = f ( x + 1 )$

Accepted Answer

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

Question 14

A real estate office handles an apartment complex with 60 units.When the rent per unit is $98 per month, all 60 units are occupied.However, when the rent is $630 per month, the average number of occupied units drops to 46.Assume that the relationship between the monthly rent p and the demand x is linear. Select the equation of the line giving the demand x in terms of the rent p.

Accepted Answer

A) x = 532p + 62.58 
B) x = -38p - 62.58 
C) x = $- \frac { 1 } { 38 }$ p + 62.58 
D) x = -38p + 62.58 
E) x = 14p + 62.58 
A) x = 532p + 62.58 
B) x = -38p - 62.58 
C) x = $- \frac { 1 } { 38 }$ p + 62.58 
D) x = -38p + 62.58 
E) x = 14p + 62.58

Question 15

For following function, select (on the same set of coordinate axes) a graph of function for $c = 3,1 \text { and } - 3$ .   $f ( x ) = \left\{ \begin{array} { l } 
x ^ { 2 } + c , x < 0 \
- x ^ { 2 } + c , x \geq 0
\end{array} \right.$

Accepted Answer

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

Question 16

Use the viewing window shown to select a possible equation for the transformation of the parent function.

Accepted Answer

A)  $y = \sqrt { x } - 5$ 
B)  $y = - \sqrt { x } + 5$ 
C)  $y = - \sqrt { x } - 5$ 
D)  $y = \sqrt { x } + 5$ 
E)  $y = - \sqrt { x } - 6$ 
A)  $y = \sqrt { x } - 5$ 
B)  $y = - \sqrt { x } + 5$ 
C)  $y = - \sqrt { x } - 5$ 
D)  $y = \sqrt { x } + 5$ 
E)  $y = - \sqrt { x } - 6$

Question 17

The graph of a function is sketched below. ​   ​
Determine the interval on which the function is decreasing.
​

Accepted Answer

A) (-∞, -3] ∩ [-1, ∞) 
B) ​[-3, -1] 
C) ​[-1, -1]​ 
D) ​[1, 3]​ 
E) (-∞, -3] ∩ [-1, ∞)​ 
A) (-∞, -3] ∩ [-1, ∞) 
B) ​[-3, -1] 
C) ​[-1, -1]​ 
D) ​[1, 3]​ 
E) (-∞, -3] ∩ [-1, ∞)​

Question 18

Find (f + g)(x).  $f ( x ) = 2 x - 3 , g ( x ) = 4 - x$

Accepted Answer

A)  $3 x - 1$ 
B)  $2 x - 1$ 
C)  $2 x + 1$ 
D)  $3 x + 1$ 
E)  $x + 1$ 
A)  $3 x - 1$ 
B)  $2 x - 1$ 
C)  $2 x + 1$ 
D)  $3 x + 1$ 
E)  $x + 1$

Question 19

Write the standard form of the equation of the circle with center (5, -7) and radius 5.

Accepted Answer

A)   $( x + 5 ) ^ { 2 } + ( y - 7 ) ^ { 2 } = 5$ 
B)  $( x - 5 ) ^ { 2 } + ( y + 7 ) ^ { 2 } = 5$ 
C)  $( x - 5 ) ^ { 2 } + ( y + 7 ) ^ { 2 } = 25$ 
D)  $( x + 5 ) ^ { 2 } + ( y - 7 ) ^ { 2 } = 25$ 
E)  $( x - 5 ) ^ { 2 } + ( y - 7 ) ^ { 2 } = 25$ 
A)   $( x + 5 ) ^ { 2 } + ( y - 7 ) ^ { 2 } = 5$ 
B)  $( x - 5 ) ^ { 2 } + ( y + 7 ) ^ { 2 } = 5$ 
C)  $( x - 5 ) ^ { 2 } + ( y + 7 ) ^ { 2 } = 25$ 
D)  $( x + 5 ) ^ { 2 } + ( y - 7 ) ^ { 2 } = 25$ 
E)  $( x - 5 ) ^ { 2 } + ( y - 7 ) ^ { 2 } = 25$

Question 20

Use a graphing utility to graph the equation.Use a standard setting.Approximate any intercepts. ​
Y = |x + 2|
​

Accepted Answer

A) Intercepts: (0, -2), (0, 2)​   
B) ​Intercepts: (-2, 0), (0, -2)​   
C) ​Intercepts: (2, 0), (0, 2)​   
D) Intercepts: (-2, 0), (0, 2)​   
E) ​Intercepts: (-2, 0), (2, 0)​   
A) Intercepts: (0, -2), (0, 2)​   
B) ​Intercepts: (-2, 0), (0, -2)​   
C) ​Intercepts: (2, 0), (0, 2)​   
D) Intercepts: (-2, 0), (0, 2)​   
E) ​Intercepts: (-2, 0), (2, 0)​

Find the slope of the line passing through the pair of points. P (-9, 14); Q (-18, -2)

Determine whether the function is one-to-one. Y = (x - 5)²; x ≥ 5

Identify any intercepts and test for symmetry.Then sketch the graph of the equation. $y = x ^ { 3 } - 6$

Evaluate the function f(x) = [[3x + 1]] for x = 4.

Find the average rate of change of the function from x₁ = 0 to x₂ = 3. $f ( x ) = 3 x + 10$

Which function does the graph represent

Select the correct graph, showing f and g are inverse functions. $f ( x ) = \sqrt { x - 3 } , g ( x ) = x ^ { 2 } + 3 , x \geq 0$

Let S represent the midpoint between (5, 3) and (-5, -7).Let T represent the midpoint between (5, 3) and S.Find the coordinates of T.

Select the graph of the function and determine whether it is even, odd, or neither. $f ( x ) = \sqrt { 3 - x }$

Graphically estimate the x- and y-intercepts of the graph. $y = 81 - 9 x ^ { 2 }$ $Graphically estimate the x- and y-intercepts of the graph. y = 81 - 9 x ^ { 2 }$

Find (f - g)(x). $f ( x ) = x + 3 , g ( x ) = x - 3$

Use the graph of $f ( x ) = x ^ { 2 }$ to write an equation for the function whose graph is shown. $Use the graph of f ( x ) = x ^ { 2 } to write an equation for the function whose graph is shown.$

Use the given graph of f to select the graph for following function. $y = f ( x + 1 )$

For following function, select (on the same set of coordinate axes) a graph of function for $c = 3,1 \text { and } - 3$ . $f ( x ) = \left\{ \begin{array} { l } x ^ { 2 } + c , x < 0 \\- x ^ { 2 } + c , x \geq 0\end{array} \right.$

Use the viewing window shown to select a possible equation for the transformation of the parent function.

The graph of a function is sketched below. Determine the interval on which the function is decreasing.

Find (f + g)(x). $f ( x ) = 2 x - 3 , g ( x ) = 4 - x$

Write the standard form of the equation of the circle with center (5, -7) and radius 5.

Use a graphing utility to graph the equation.Use a standard setting.Approximate any intercepts. Y = |x + 2|

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

Find the slope of the line passing through the pair of points. P (-9, 14); Q (-18, -2)

Determine whether the function is one-to-one. ​ Y = (x - 5)2; x ≥ 5 ​

Identify any intercepts and test for symmetry.Then sketch the graph of the equation. y=x3−6y = x ^ { 3 } - 6y=x3−6

Evaluate the function f(x) = [[3x + 1]] for x = 4. ​

Find the average rate of change of the function from x1 = 0 to x2 = 3. f(x)=3x+10f ( x ) = 3 x + 10f(x)=3x+10

Which function does the graph represent

Select the correct graph, showing f and g are inverse functions. f(x)=x−3,g(x)=x2+3,x≥0f ( x ) = \sqrt { x - 3 } , g ( x ) = x ^ { 2 } + 3 , x \geq 0f(x)=x−3​,g(x)=x2+3,x≥0

Let S represent the midpoint between (5, 3) and (-5, -7).Let T represent the midpoint between (5, 3) and S.Find the coordinates of T. ​

Select the graph of the function and determine whether it is even, odd, or neither. f(x)=3−xf ( x ) = \sqrt { 3 - x }f(x)=3−x​

Graphically estimate the x- and y-intercepts of the graph. y=81−9x2y = 81 - 9 x ^ { 2 }y=81−9x2

Find (f - g)(x). f(x)=x+3,g(x)=x−3f ( x ) = x + 3 , g ( x ) = x - 3f(x)=x+3,g(x)=x−3

Use the graph of f(x)=x2f ( x ) = x ^ { 2 }f(x)=x2 to write an equation for the function whose graph is shown.

Use the given graph of f to select the graph for following function. y=f(x+1)y = f ( x + 1 )y=f(x+1)

Use the viewing window shown to select a possible equation for the transformation of the parent function.

The graph of a function is sketched below. ​ ​ Determine the interval on which the function is decreasing. ​

Find (f + g)(x). f(x)=2x−3,g(x)=4−xf ( x ) = 2 x - 3 , g ( x ) = 4 - xf(x)=2x−3,g(x)=4−x

Write the standard form of the equation of the circle with center (5, -7) and radius 5.

Use a graphing utility to graph the equation.Use a standard setting.Approximate any intercepts. ​ Y = |x + 2| ​

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

Determine whether the function is one-to-one. Y = (x - 5)²; x ≥ 5

Identify any intercepts and test for symmetry.Then sketch the graph of the equation. $y = x ^ { 3 } - 6$

Evaluate the function f(x) = [[3x + 1]] for x = 4.

Find the average rate of change of the function from x₁ = 0 to x₂ = 3. $f ( x ) = 3 x + 10$

Select the correct graph, showing f and g are inverse functions. $f ( x ) = \sqrt { x - 3 } , g ( x ) = x ^ { 2 } + 3 , x \geq 0$

Let S represent the midpoint between (5, 3) and (-5, -7).Let T represent the midpoint between (5, 3) and S.Find the coordinates of T.

Select the graph of the function and determine whether it is even, odd, or neither. $f ( x ) = \sqrt { 3 - x }$

Graphically estimate the x- and y-intercepts of the graph. $y = 81 - 9 x ^ { 2 }$ $Graphically estimate the x- and y-intercepts of the graph. y = 81 - 9 x ^ { 2 }$

Find (f - g)(x). $f ( x ) = x + 3 , g ( x ) = x - 3$

Use the graph of $f ( x ) = x ^ { 2 }$ to write an equation for the function whose graph is shown. $Use the graph of f ( x ) = x ^ { 2 } to write an equation for the function whose graph is shown.$

Use the given graph of f to select the graph for following function. $y = f ( x + 1 )$

The graph of a function is sketched below. Determine the interval on which the function is decreasing.

Find (f + g)(x). $f ( x ) = 2 x - 3 , g ( x ) = 4 - x$

Use a graphing utility to graph the equation.Use a standard setting.Approximate any intercepts. Y = |x + 2|