Question 1

Evaluate the indicated function for $f ( x ) = x ^ { 2 } + 2$ and $g ( x ) = x - 4$ .   $( f + g ) ( 3 )$

Accepted Answer

A) 12 
B) -10 
C) 7 
D) 14 
E) 10 
A) 12 
B) -10 
C) 7 
D) 14 
E) 10

Question 2

Find the average rate of change of the function from x1 = 1 to x2 = 3.   $f ( x ) = x ^ { 3 } - 8 x ^ { 2 } - x$

Accepted Answer

A) The average rate of change from x1 = 1 to x2 = 3 is 19. 
B) The average rate of change from x1 = 1 to x2 = 3 is -20. 
C) The average rate of change from x1 = 1 to x2 = 3 is 8. 
D) The average rate of change from x1 = 1 to x2 = 3 is -14. 
E) The average rate of change from x1 = 1 to x2 = 3 is 14. 
A) The average rate of change from x1 = 1 to x2 = 3 is 19. 
B) The average rate of change from x1 = 1 to x2 = 3 is -20. 
C) The average rate of change from x1 = 1 to x2 = 3 is 8. 
D) The average rate of change from x1 = 1 to x2 = 3 is -14. 
E) The average rate of change from x1 = 1 to x2 = 3 is 14.

Question 3

Select the graph of the function. $f ( x ) = \left\{ \begin{array} { l l } 
2 x + 1 & x < 0 \
1 - x & x \geq 0
\end{array} \right.$

Accepted Answer

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

Question 4

Find the center and radius of the circle with equation $( x + 7 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = 25$ .

Accepted Answer

A) Center: (7, 2)Radius: 5 
B) Center: (-7, 2)Radius: 25 
C) Center: (7, -2)Radius: 25 
D) Center: (7, -2)Radius: 5 
E) Center: (-7, 2)Radius: 5 
A) Center: (7, 2)Radius: 5 
B) Center: (-7, 2)Radius: 25 
C) Center: (7, -2)Radius: 25 
D) Center: (7, -2)Radius: 5 
E) Center: (-7, 2)Radius: 5

Question 5

Plot the points below whose coordinates are given on a Cartesian coordinate system. ​
(5, 2), (9, -6), (2, -4), (9, -5)
​

Accepted Answer

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

Question 6

An airplane flies from one city in a straight line to another city, which is 360 kilometers north and 150 kilometers west of first city.How far does the plane fly  ?

Accepted Answer

A) 150 km 
B) 390 km 
C) 255 km 
D) 360 km 
E) 350 km 
A) 150 km 
B) 390 km 
C) 255 km 
D) 360 km 
E) 350 km

Question 7

Write the standard form of the equation of the circle which has (-5, 4) and (-1, 8) as endpoints of a diameter.

Accepted Answer

A)  $( x + 3 ) ^ { 2 } + ( y - 6 ) ^ { 2 } = \sqrt { 8 }$ 
B)  $( x - 3 ) ^ { 2 } + ( y + 6 ) ^ { 2 } = 8$ 
C)  $( x - 3 ) ^ { 2 } + ( y - 6 ) ^ { 2 } = 8$ 
D)  $( x - 3 ) ^ { 2 } + ( y - 6 ) ^ { 2 } = \sqrt { 8 }$ 
E)  $( x + 3 ) ^ { 2 } + ( y - 6 ) ^ { 2 } = 8$ 
A)  $( x + 3 ) ^ { 2 } + ( y - 6 ) ^ { 2 } = \sqrt { 8 }$ 
B)  $( x - 3 ) ^ { 2 } + ( y + 6 ) ^ { 2 } = 8$ 
C)  $( x - 3 ) ^ { 2 } + ( y - 6 ) ^ { 2 } = 8$ 
D)  $( x - 3 ) ^ { 2 } + ( y - 6 ) ^ { 2 } = \sqrt { 8 }$ 
E)  $( x + 3 ) ^ { 2 } + ( y - 6 ) ^ { 2 } = 8$

Question 8

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

Accepted Answer

A)  $y = | x | + 6$ 
B)  $y = | x | - 5$ 
C)  $y = | x | - 6$ 
D)  $y = | x | + 7$ 
E)  $y = | x | + 5$ 
A)  $y = | x | + 6$ 
B)  $y = | x | - 5$ 
C)  $y = | x | - 6$ 
D)  $y = | x | + 7$ 
E)  $y = | x | + 5$

Question 9

Find the slope of the line passing through the pair of points.  
(-1, -8), (3, 7)

Accepted Answer

A)    m = $- \frac { 1 } { 2 }$ 
B)    m = $\frac { 15 } { 4 }$ 
C)    m = - $\frac { 4 } { 15 }$ 
D)    m = - $\frac { 15 } { 4 }$ 
E)    m = $\frac { 4 } { 15 }$ 
A)    m = $- \frac { 1 } { 2 }$ 
B)    m = $\frac { 15 } { 4 }$ 
C)    m = - $\frac { 4 } { 15 }$ 
D)    m = - $\frac { 15 } { 4 }$ 
E)    m = $\frac { 4 } { 15 }$

Question 10

Find the midpoint between the two points (-19, 9) and (11, 13). ​

Accepted Answer

A) (-15, 2) 
B) (-15, 11) 
C) (-8, 11) 
D) (-4, 2) 
E) (-4, 11) 
A) (-15, 2) 
B) (-15, 11) 
C) (-8, 11) 
D) (-4, 2) 
E) (-4, 11)

Question 11

Identify any intercepts and test for symmetry.Then sketch the graph of the equation. ​
Y = |x - 4|
​

Accepted Answer

A) x- intercept: (4, 0)y- intercept: (0, 4)No symmetry​   ​ 
B) x- intercept: (-4, 0)y- intercept: (0, 4)No symmetry​   
C) x- intercept: (4, 0)y- intercept: (4, 0)No symmetry​   
D) x- intercept: (4, 0)y- intercept: (0, 4)No symmetry​   
E) x- intercept: (4, 0)y- intercept: (4, 0)No symmetry​   
A) x- intercept: (4, 0)y- intercept: (0, 4)No symmetry​   ​ 
B) x- intercept: (-4, 0)y- intercept: (0, 4)No symmetry​   
C) x- intercept: (4, 0)y- intercept: (4, 0)No symmetry​   
D) x- intercept: (4, 0)y- intercept: (0, 4)No symmetry​   
E) x- intercept: (4, 0)y- intercept: (4, 0)No symmetry​

Question 12

Find the coordinates of a second point on the graph of a function f if the given point is on the graph and the function is even. ​
(-x, y)
​

Accepted Answer

A) (-x, -y) 
B) (x, -y) 
C) (-x, y) 
D) (x, y) 
E) None of the above 
A) (-x, -y) 
B) (x, -y) 
C) (-x, y) 
D) (x, y) 
E) None of the above

Question 13

Find the slope and y-intercept (if possible) of the equation of the line.Select the correct answer for the line.  $y = x - 3$

Accepted Answer

A)    
m = -1y-intercept: (0, 3) 
B)    
m = 1y-intercept: (0, -3) 
C)    
 m is undefined.y-intercept: (0, 3) 
D)     
m = 3y-intercept: (0, 3) 
E)     
m = -3y-intercept: (0, -3) 
A)    
m = -1y-intercept: (0, 3) 
B)    
m = 1y-intercept: (0, -3) 
C)    
 m is undefined.y-intercept: (0, 3) 
D)     
m = 3y-intercept: (0, 3) 
E)     
m = -3y-intercept: (0, -3)

Question 14

Determine the intervals over which the function is increasing, decreasing, or constant. $$f ( x ) = \left\{ \begin{array} { l } 
- x ^ { 2 } , x < 1 \
x ^ { 2 } - 2 x + 2 , x \geq 1
\end{array} \right.$$

Accepted Answer

A)  constant on (-$\infty$, 0)increasing on (0, $\infty$) 
B) increasing on (-$\infty$, 0), (1, $\infty$)descreasing on (0, 1) 
C)  constant on (-$\infty$, 1)increasing on (1, $\infty$) 
D)  constant on (-$\infty$, 1)descreasing on (1, $\infty$) 
E)  constant on (-$\infty$, 0)descreasing on (0, 1) 
A)  constant on (-$\infty$, 0)increasing on (0, $\infty$) 
B) increasing on (-$\infty$, 0), (1, $\infty$)descreasing on (0, 1) 
C)  constant on (-$\infty$, 1)increasing on (1, $\infty$) 
D)  constant on (-$\infty$, 1)descreasing on (1, $\infty$) 
E)  constant on (-$\infty$, 0)descreasing on (0, 1)

Question 15

Determine the quadrant(s) in which (x, y) is located so that the condition(s) is (are) satisfied. ​
Xy < -4
​

Accepted Answer

A) Quadrant II or III 
B) Quadrant I or III 
C) Quadrant III or IV 
D) Quadrant II or IV 
E) Quadrant I or IV 
A) Quadrant II or III 
B) Quadrant I or III 
C) Quadrant III or IV 
D) Quadrant II or IV 
E) Quadrant I or IV

Question 16

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)  $y = \sqrt { x } - 4$ 
C)  $y = \sqrt { x } + 4$ 
D)  $y = \sqrt { x } - 3$ 
E)  $y = \sqrt { x } + 3$ 
A)  $y = \sqrt { x } + 5$ 
B)  $y = \sqrt { x } - 4$ 
C)  $y = \sqrt { x } + 4$ 
D)  $y = \sqrt { x } - 3$ 
E)  $y = \sqrt { x } + 3$

Question 17

Determine whether the function has an inverse function.If it does, find the inverse function.  
G(x) = x7

Accepted Answer

A)  $g ^ { - 1 } ( x ) = \frac { 7 } { x }$ 
B) g-1(x) = -7x 
C)   $g ^ { - 1 } ( x ) = - \frac { x } { 7 }$ 
D) g-1(x) = 7x 
E) The inverse exists, but none of the above 
A)  $g ^ { - 1 } ( x ) = \frac { 7 } { x }$ 
B) g-1(x) = -7x 
C)   $g ^ { - 1 } ( x ) = - \frac { x } { 7 }$ 
D) g-1(x) = 7x 
E) The inverse exists, but none of the above

Question 18

Let $f ( x ) = \sqrt { x + 1 } , g ( x ) = x ^ { 2 } - 1$ .Find the composite function.
​ $( f \circ g ) ( x )$

Accepted Answer

The answer of Let \(f ( x ) = \sqrt...

Question 19

Assume that y is directly proportional to x.Use the given x-value and y-value to find a linear model that relates y and x. 
 $x = 38 , y = 2400$

Accepted Answer

A) y = $\frac { 1200 } { 19 }$ x 
B) y = - 2400x 
C) y = $\frac { 19 } { 1200 }$ x 
D) y = - $\frac { 19 } { 1200 }$ x 
E) y = - $\frac { 1200 } { 19 }$ x 
A) y = $\frac { 1200 } { 19 }$ x 
B) y = - 2400x 
C) y = $\frac { 19 } { 1200 }$ x 
D) y = - $\frac { 19 } { 1200 }$ x 
E) y = - $\frac { 1200 } { 19 }$ x

Question 20

Find the inverse function of f informally.  
F(x) = x - 5

Accepted Answer

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

Evaluate the indicated function for $f ( x ) = x ^ { 2 } + 2$ and $g ( x ) = x - 4$ . $( f + g ) ( 3 )$

Find the average rate of change of the function from x₁ = 1 to x₂ = 3. $f ( x ) = x ^ { 3 } - 8 x ^ { 2 } - x$

Select the graph of the function. $f ( x ) = \left\{ \begin{array} { l l } 2 x + 1 & x < 0 \\1 - x & x \geq 0\end{array} \right.$

Find the center and radius of the circle with equation $( x + 7 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = 25$ .

Plot the points below whose coordinates are given on a Cartesian coordinate system. (5, 2), (9, -6), (2, -4), (9, -5)

An airplane flies from one city in a straight line to another city, which is 360 kilometers north and 150 kilometers west of first city.How far does the plane fly ?

Write the standard form of the equation of the circle which has (-5, 4) and (-1, 8) as endpoints of a diameter.

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

Find the slope of the line passing through the pair of points. (-1, -8), (3, 7)

Find the midpoint between the two points (-19, 9) and (11, 13).

Identify any intercepts and test for symmetry.Then sketch the graph of the equation. Y = |x - 4|

Find the coordinates of a second point on the graph of a function f if the given point is on the graph and the function is even. (-x, y)

Find the slope and y-intercept (if possible) of the equation of the line.Select the correct answer for the line. $y = x - 3$

Determine the quadrant(s) in which (x, y) is located so that the condition(s) is (are) satisfied. Xy < -4

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

Determine whether the function has an inverse function.If it does, find the inverse function. G(x) = x⁷

Let $f ( x ) = \sqrt { x + 1 } , g ( x ) = x ^ { 2 } - 1$ .Find the composite function. $( f \circ g ) ( x )$

Assume that y is directly proportional to x.Use the given x-value and y-value to find a linear model that relates y and x. $x = 38 , y = 2400$

Find the inverse function of f informally. F(x) = x - 5

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

Evaluate the indicated function for f(x)=x2+2f ( x ) = x ^ { 2 } + 2f(x)=x2+2 and g(x)=x−4g ( x ) = x - 4g(x)=x−4 . (f+g)(3)( f + g ) ( 3 )(f+g)(3)

Find the average rate of change of the function from x1 = 1 to x2 = 3. f(x)=x3−8x2−xf ( x ) = x ^ { 3 } - 8 x ^ { 2 } - xf(x)=x3−8x2−x

Select the graph of the function. f(x)={2x+1x<01−xx≥0f ( x ) = \left\{ \begin{array} { l l } 2 x + 1 & x < 0 \\1 - x & x \geq 0\end{array} \right.f(x)={2x+11−x​x<0x≥0​

Find the center and radius of the circle with equation (x+7)2+(y−2)2=25( x + 7 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = 25(x+7)2+(y−2)2=25 .

Plot the points below whose coordinates are given on a Cartesian coordinate system. ​ (5, 2), (9, -6), (2, -4), (9, -5) ​

An airplane flies from one city in a straight line to another city, which is 360 kilometers north and 150 kilometers west of first city.How far does the plane fly ?

Write the standard form of the equation of the circle which has (-5, 4) and (-1, 8) as endpoints of a diameter.

Use the graph of f(x)=∣x∣f ( x ) = | x |f(x)=∣x∣ to write an equation for the function whose graph is shown.

Find the slope of the line passing through the pair of points. (-1, -8), (3, 7)

Find the midpoint between the two points (-19, 9) and (11, 13). ​

Identify any intercepts and test for symmetry.Then sketch the graph of the equation. ​ Y = |x - 4| ​

Find the coordinates of a second point on the graph of a function f if the given point is on the graph and the function is even. ​ (-x, y) ​

Find the slope and y-intercept (if possible) of the equation of the line.Select the correct answer for the line. y=x−3y = x - 3y=x−3

Determine the intervals over which the function is increasing, decreasing, or constant. f(x)={−x2,x<1x2−2x+2,x≥1f ( x ) = \left\{ \begin{array} { l } - x ^ { 2 } , x < 1 \\x ^ { 2 } - 2 x + 2 , x \geq 1\end{array} \right.f(x)={−x2,x<1x2−2x+2,x≥1​

Determine the quadrant(s) in which (x, y) is located so that the condition(s) is (are) satisfied. ​ Xy < -4 ​

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

Determine whether the function has an inverse function.If it does, find the inverse function. G(x) = x7

Let f(x)=x+1,g(x)=x2−1f ( x ) = \sqrt { x + 1 } , g ( x ) = x ^ { 2 } - 1f(x)=x+1​,g(x)=x2−1 .Find the composite function. ​ (f∘g)(x)( f \circ g ) ( x )(f∘g)(x)

Assume that y is directly proportional to x.Use the given x-value and y-value to find a linear model that relates y and x. x=38,y=2400x = 38 , y = 2400x=38,y=2400

Find the inverse function of f informally. F(x) = x - 5

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

Evaluate the indicated function for $f ( x ) = x ^ { 2 } + 2$ and $g ( x ) = x - 4$ . $( f + g ) ( 3 )$

Find the average rate of change of the function from x₁ = 1 to x₂ = 3. $f ( x ) = x ^ { 3 } - 8 x ^ { 2 } - x$

Select the graph of the function. $f ( x ) = \left\{ \begin{array} { l l } 2 x + 1 & x < 0 \\1 - x & x \geq 0\end{array} \right.$

Find the center and radius of the circle with equation $( x + 7 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = 25$ .

Plot the points below whose coordinates are given on a Cartesian coordinate system. (5, 2), (9, -6), (2, -4), (9, -5)

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

Find the midpoint between the two points (-19, 9) and (11, 13).

Identify any intercepts and test for symmetry.Then sketch the graph of the equation. Y = |x - 4|

Find the coordinates of a second point on the graph of a function f if the given point is on the graph and the function is even. (-x, y)

Find the slope and y-intercept (if possible) of the equation of the line.Select the correct answer for the line. $y = x - 3$

Determine the quadrant(s) in which (x, y) is located so that the condition(s) is (are) satisfied. Xy < -4

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

Determine whether the function has an inverse function.If it does, find the inverse function. G(x) = x⁷

Let $f ( x ) = \sqrt { x + 1 } , g ( x ) = x ^ { 2 } - 1$ .Find the composite function. $( f \circ g ) ( x )$

Assume that y is directly proportional to x.Use the given x-value and y-value to find a linear model that relates y and x. $x = 38 , y = 2400$