Question 1

Determine whether the lines are parallel, perpendicular, or neither.  
L1: y = $\frac { 1 } { 3 }$ x - 4
L2: y = $\frac { 1 } { 3 }$ x - 3

Accepted Answer

A) Perpendicular 
B) Parallel 
C) Neither 
A) Perpendicular 
B) Parallel 
C) Neither

Question 2

Select the graph of the function and find the zeros of the function. 
 $f ( x ) = \sqrt { 2 x + 3 }$

Accepted Answer

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

Question 3

The graph shows the average salaries for senior high school principals from 1996 through 2008. ​   ​
Find the slope of the line segment connecting the points for the years 1998 and 2002.
​

Accepted Answer

A) -2394 
B) 2391 
C) -2391 
D) 2396 
E) 2392 
A) -2394 
B) 2391 
C) -2391 
D) 2396 
E) 2392

Question 4

Select the correct graph of the given function.
 $f ( x ) = 2 - x ^ { 2 }$

Accepted Answer

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

Question 5

Find the inverse of the one-to-one function.  $y = \frac { 1 } { 8 x }$

Accepted Answer

A)  $f ^ { - 1 } ( x ) = \frac { 8 } { x }$ 
B)  $f ^ { - 1 } ( x ) = \frac { x } { 8 }$ 
C)  $f ^ { - 1 } ( x ) = 8 x$ 
D)  $f ^ { - 1 } ( x ) = \frac { 1 } { 8 x }$ 
E) inverse does not exist 
A)  $f ^ { - 1 } ( x ) = \frac { 8 } { x }$ 
B)  $f ^ { - 1 } ( x ) = \frac { x } { 8 }$ 
C)  $f ^ { - 1 } ( x ) = 8 x$ 
D)  $f ^ { - 1 } ( x ) = \frac { 1 } { 8 x }$ 
E) inverse does not exist

Question 6

Use the fact that the resistance of a wire carrying an electrical current is directly proportional to its length and inversely proportional to its cross-sectional area. ​
A 10-foot piece of copper wire produces a resistance of 0.2 ohm.Use the constant of proportionality k = 0.000833 to find the diameter of the wire.
​
(Round the answer up to three decimal places.)
​

Accepted Answer

A) 0.23 ft 
B) 0.58 ft 
C) 0.38 ft 
D) 0.48 ft 
E) 0.73 ft 
A) 0.23 ft 
B) 0.58 ft 
C) 0.38 ft 
D) 0.48 ft 
E) 0.73 ft

Question 7

Select the graph of the function and determine whether it is even, odd, or neither. ​
F(x) = |x + 6|
​

Accepted Answer

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

Question 8

Given points(-1,1), and (-11,-9) form the vertices of the base of a triangle, find a third point so that the three points form the vertices of an isosceles triangle. ​

Accepted Answer

A) (3, 1) 
B) (4, -15) 
C) ​(-15, -13) 
D) ​(3, 5) 
E) ​(-6, -4) 
A) (3, 1) 
B) (4, -15) 
C) ​(-15, -13) 
D) ​(3, 5) 
E) ​(-6, -4)

Question 9

Use a graphing utility to graph the equation.Use a standard setting.Approximate any intercepts. 
 $y = 7 - \frac { 1 } { 2 } x$

Accepted Answer

A)  Intercepts: (0, 7), (-14, 0)    
B) Intercepts: (-14, 0), (0, -7)    
C)  Intercepts: (14, 0), (0, -7)    
D)  Intercepts: (0, 8), (15, 0)    
E)  Intercepts: (14, 0), (0, 7)    
A)  Intercepts: (0, 7), (-14, 0)    
B) Intercepts: (-14, 0), (0, -7)    
C)  Intercepts: (14, 0), (0, -7)    
D)  Intercepts: (0, 8), (15, 0)    
E)  Intercepts: (14, 0), (0, 7)

Question 10

​Use the position equation s = -16t2 + v0t + s0 to write a function that represents the situation and give the average velocity of the object from time t1 to time t2. An object is thrown upward from a height of 38 feet at a velocity of 84 feet per second.
T1 = 1, t2 = 3

Accepted Answer

A) ​s = -16t2 + 38t + 84; avg. velocity = 79 ft/s 
B) ​s = -16t2 + 84t + 38; avg. velocity = 125 ft/s 
C) ​s = -16t2 + 38t + 84; avg. velocity = -26 ft/s 
D) ​s = -16t2 + 84t + 38; avg. velocity = 20 ft/s 
E) ​s = -16t2 + 84t + 38; avg. velocity = 40 ft/s 
A) ​s = -16t2 + 38t + 84; avg. velocity = 79 ft/s 
B) ​s = -16t2 + 84t + 38; avg. velocity = 125 ft/s 
C) ​s = -16t2 + 38t + 84; avg. velocity = -26 ft/s 
D) ​s = -16t2 + 84t + 38; avg. velocity = 20 ft/s 
E) ​s = -16t2 + 84t + 38; avg. velocity = 40 ft/s

Question 11

Let $f ( x ) = \frac { 1 } { x } , g ( x ) = x + 5$ .Find the composite function which expresses the given correspondence correctly. 
 $\frac { 1 } { x + 5 }$

Accepted Answer

A)  $( g \circ g ) ( x )$ 
B)  $( g \circ f ) ( x )$ 
C)  $( f \circ f ) ( x )$ 
D)  $( f \circ g ) ( x )$ 
E) none of the above 
A)  $( g \circ g ) ( x )$ 
B)  $( g \circ f ) ( x )$ 
C)  $( f \circ f ) ( x )$ 
D)  $( f \circ g ) ( x )$ 
E) none of the above

Question 12

For following function, select (on the same set of coordinate axes) a graph for $c = - 3 , - 5 \text { and } - 1$ .   $f ( x ) = \sqrt { x + c }$

Accepted Answer

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

Question 13

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. 
 $\left( - \frac { 1 } { 2 } , 5 \right)$

Accepted Answer

A)  $\left( - \frac { 1 } { 2 } , - 5 \right)$ 
B)  $\left( \frac { 1 } { 2 } , 5 \right)$ 
C)  $\left( \frac { 1 } { 2 } , - 5 \right)$ 
D)  $\left( - \frac { 1 } { 2 } , 5 \right)$ 
E) None of the above 
A)  $\left( - \frac { 1 } { 2 } , - 5 \right)$ 
B)  $\left( \frac { 1 } { 2 } , 5 \right)$ 
C)  $\left( \frac { 1 } { 2 } , - 5 \right)$ 
D)  $\left( - \frac { 1 } { 2 } , 5 \right)$ 
E) None of the above

Question 14

Find the graph of the equation. ​
F (x) = | x - 2 |
​

Accepted Answer

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

Question 15

Show that the points form the vertices of the indicated polygon.  
Isosceles triangle: (7, 1), (5, 4), (2, 6)

Accepted Answer

A) Distances between the points: $\sqrt { 19 } , \sqrt { 13 } , \sqrt { 50 }$ 
B) Distances between the points: $\sqrt { 13 } , \sqrt { 13 } , \sqrt { 50 }$ 
C) Distances between the points: $\sqrt { 43 } , \sqrt { 13 } , \sqrt { 50 }$ 
D) Distances between the points: $\sqrt { 26 } , \sqrt { 13 } , \sqrt { 50 }$ 
E) Distances between the points: $\sqrt { 37 } , \sqrt { 13 } , \sqrt { 50 }$ 
A) Distances between the points: $\sqrt { 19 } , \sqrt { 13 } , \sqrt { 50 }$ 
B) Distances between the points: $\sqrt { 13 } , \sqrt { 13 } , \sqrt { 50 }$ 
C) Distances between the points: $\sqrt { 43 } , \sqrt { 13 } , \sqrt { 50 }$ 
D) Distances between the points: $\sqrt { 26 } , \sqrt { 13 } , \sqrt { 50 }$ 
E) Distances between the points: $\sqrt { 37 } , \sqrt { 13 } , \sqrt { 50 }$

Question 16

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. 
 $x = 2 , y = 58$

Accepted Answer

A)  $y = 29 x$ 
B)  $y = - 29 x$ 
C)  $y = 58 x$ 
D)  $y = - 58 x$ 
E)  $y = 29$ 
A)  $y = 29 x$ 
B)  $y = - 29 x$ 
C)  $y = 58 x$ 
D)  $y = - 58 x$ 
E)  $y = 29$

Question 17

Select the graph of f and f-1 on the same set of coordinate axes. ​
F(x) = 2x - 3
​

Accepted Answer

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

Question 18

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

Accepted Answer

A)   $f ( x ) = - 3 | x - 2 | + 2$ 
B)  $f ( x ) = - 3 | x + 2 | + 2$ 
C)  $f ( x ) = | - 3 x + 2 | + 2$ 
D)  $f ( x ) = - 3 | x + 2 | - 2$ 
E)  $f ( x ) = | - 3 x - 2 | + 2$ 
A)   $f ( x ) = - 3 | x - 2 | + 2$ 
B)  $f ( x ) = - 3 | x + 2 | + 2$ 
C)  $f ( x ) = | - 3 x + 2 | + 2$ 
D)  $f ( x ) = - 3 | x + 2 | - 2$ 
E)  $f ( x ) = | - 3 x - 2 | + 2$

Question 19

Find $g \circ f$ and the domain of the composite function. 
 $f ( x ) = x ^ { 2 } + 4 , g ( x ) = \sqrt { x }$

Accepted Answer

A)  $( x + 4 ) ^ { 4 }$ Domain of $g \circ f$ : all real numbers x 
B)  $( x - 4 ) ^ { 4 }$ Domain of $g \circ f$ : all real numbers x 
C)  $\sqrt { x ^ { 2 } + 4 }$ Domain of $g \circ f$ : all real numbers x 
D)  $\sqrt { ( x - 4 ) ^ { 4 } }$ Domain of $g \circ f$ : all real numbers x 
E)  $\sqrt { ( x + 4 ) ^ { 4 } }$ Domain of $g \circ f$ : all real numbers x 
A)  $( x + 4 ) ^ { 4 }$ Domain of $g \circ f$ : all real numbers x 
B)  $( x - 4 ) ^ { 4 }$ Domain of $g \circ f$ : all real numbers x 
C)  $\sqrt { x ^ { 2 } + 4 }$ Domain of $g \circ f$ : all real numbers x 
D)  $\sqrt { ( x - 4 ) ^ { 4 } }$ Domain of $g \circ f$ : all real numbers x 
E)  $\sqrt { ( x + 4 ) ^ { 4 } }$ Domain of $g \circ f$ : all real numbers x

Question 20

Find the difference quotient and simplify your answer.  
F(x) = x2 - x + 1, $\frac { f ( 6 + h ) - f ( 6 ) } { h }$ , h $\neq$  0

Accepted Answer

A)  $\frac { f ( 6 + h ) - f ( 6 ) } { h } = h + 11$ , h $\neq$  0 
B)  $\frac { f ( 6 + h ) - f ( 6 ) } { h } = h + 15$ , h $\neq$  0 
C)  $\frac { f ( 6 + h ) - f ( 6 ) } { h } = h + 14$ , h $\neq$ 0 
D)  $\frac { f ( 6 + h ) - f ( 6 ) } { h } = h + 12$ , h$\neq$  0 
E)  $\frac { f ( 6 + h ) - f ( 6 ) } { h } = h + 13$ , h $\neq$  0 
A)  $\frac { f ( 6 + h ) - f ( 6 ) } { h } = h + 11$ , h $\neq$  0 
B)  $\frac { f ( 6 + h ) - f ( 6 ) } { h } = h + 15$ , h $\neq$  0 
C)  $\frac { f ( 6 + h ) - f ( 6 ) } { h } = h + 14$ , h $\neq$ 0 
D)  $\frac { f ( 6 + h ) - f ( 6 ) } { h } = h + 12$ , h$\neq$  0 
E)  $\frac { f ( 6 + h ) - f ( 6 ) } { h } = h + 13$ , h $\neq$  0

Determine whether the lines are parallel, perpendicular, or neither. L1: y = $\frac { 1 } { 3 }$ x - 4 L2: y = $\frac { 1 } { 3 }$ x - 3

Select the graph of the function and find the zeros of the function. $f ( x ) = \sqrt { 2 x + 3 }$

The graph shows the average salaries for senior high school principals from 1996 through 2008. Find the slope of the line segment connecting the points for the years 1998 and 2002.

Select the correct graph of the given function. $f ( x ) = 2 - x ^ { 2 }$

Find the inverse of the one-to-one function. $y = \frac { 1 } { 8 x }$

Select the graph of the function and determine whether it is even, odd, or neither. F(x) = |x + 6|

Given points(-1,1), and (-11,-9) form the vertices of the base of a triangle, find a third point so that the three points form the vertices of an isosceles triangle.

Use a graphing utility to graph the equation.Use a standard setting.Approximate any intercepts. $y = 7 - \frac { 1 } { 2 } x$

Use the position equation s = -16t² + v₀t + s₀ to write a function that represents the situation and give the average velocity of the object from time t₁ to time t₂. An object is thrown upward from a height of 38 feet at a velocity of 84 feet per second. T₁ = 1, t₂ = 3

Let $f ( x ) = \frac { 1 } { x } , g ( x ) = x + 5$ .Find the composite function which expresses the given correspondence correctly. $\frac { 1 } { x + 5 }$

For following function, select (on the same set of coordinate axes) a graph for $c = - 3 , - 5 \text { and } - 1$ . $f ( x ) = \sqrt { x + c }$

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. $\left( - \frac { 1 } { 2 } , 5 \right)$

Find the graph of the equation. F (x) = | x - 2 |

Show that the points form the vertices of the indicated polygon. Isosceles triangle: (7, 1), (5, 4), (2, 6)

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. $x = 2 , y = 58$

Select the graph of f and f^-1 on the same set of coordinate axes. F(x) = 2x - 3

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

Find $g \circ f$ and the domain of the composite function. $f ( x ) = x ^ { 2 } + 4 , g ( x ) = \sqrt { x }$

Find the difference quotient and simplify your answer. F(x) = x² - x + 1, $\frac { f ( 6 + h ) - f ( 6 ) } { h }$ , h $\neq$ 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

Exam 1: Functions and Their Graphs

Determine whether the lines are parallel, perpendicular, or neither. L1: y = 13\frac { 1 } { 3 }31​ x - 4 L2: y = 13\frac { 1 } { 3 }31​ x - 3

Select the graph of the function and find the zeros of the function. f(x)=2x+3f ( x ) = \sqrt { 2 x + 3 }f(x)=2x+3​

The graph shows the average salaries for senior high school principals from 1996 through 2008. ​ ​ Find the slope of the line segment connecting the points for the years 1998 and 2002. ​

Select the correct graph of the given function. f(x)=2−x2f ( x ) = 2 - x ^ { 2 }f(x)=2−x2

Find the inverse of the one-to-one function. y=18xy = \frac { 1 } { 8 x }y=8x1​

Select the graph of the function and determine whether it is even, odd, or neither. ​ F(x) = |x + 6| ​

Given points(-1,1), and (-11,-9) form the vertices of the base of a triangle, find a third point so that the three points form the vertices of an isosceles triangle. ​

Use a graphing utility to graph the equation.Use a standard setting.Approximate any intercepts. y=7−12xy = 7 - \frac { 1 } { 2 } xy=7−21​x

​Use the position equation s = -16t2 + v0t + s0 to write a function that represents the situation and give the average velocity of the object from time t1 to time t2. An object is thrown upward from a height of 38 feet at a velocity of 84 feet per second. T1 = 1, t2 = 3

Let f(x)=1x,g(x)=x+5f ( x ) = \frac { 1 } { x } , g ( x ) = x + 5f(x)=x1​,g(x)=x+5 .Find the composite function which expresses the given correspondence correctly. 1x+5\frac { 1 } { x + 5 }x+51​

For following function, select (on the same set of coordinate axes) a graph for c=−3,−5 and −1c = - 3 , - 5 \text { and } - 1c=−3,−5 and −1 . f(x)=x+cf ( x ) = \sqrt { x + c }f(x)=x+c​

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. (−12,5)\left( - \frac { 1 } { 2 } , 5 \right)(−21​,5)

Find the graph of the equation. ​ F (x) = | x - 2 | ​

Show that the points form the vertices of the indicated polygon. Isosceles triangle: (7, 1), (5, 4), (2, 6)

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=2,y=58x = 2 , y = 58x=2,y=58

Select the graph of f and f-1 on the same set of coordinate axes. ​ F(x) = 2x - 3 ​

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 g∘fg \circ fg∘f and the domain of the composite function. f(x)=x2+4,g(x)=xf ( x ) = x ^ { 2 } + 4 , g ( x ) = \sqrt { x }f(x)=x2+4,g(x)=x​

Find the difference quotient and simplify your answer. F(x) = x2 - x + 1, f(6+h)−f(6)h\frac { f ( 6 + h ) - f ( 6 ) } { h }hf(6+h)−f(6)​ , h ≠\neq= 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

Determine whether the lines are parallel, perpendicular, or neither. L1: y = $\frac { 1 } { 3 }$ x - 4 L2: y = $\frac { 1 } { 3 }$ x - 3

Select the graph of the function and find the zeros of the function. $f ( x ) = \sqrt { 2 x + 3 }$

The graph shows the average salaries for senior high school principals from 1996 through 2008. Find the slope of the line segment connecting the points for the years 1998 and 2002.

Select the correct graph of the given function. $f ( x ) = 2 - x ^ { 2 }$

Find the inverse of the one-to-one function. $y = \frac { 1 } { 8 x }$

Select the graph of the function and determine whether it is even, odd, or neither. F(x) = |x + 6|

Given points(-1,1), and (-11,-9) form the vertices of the base of a triangle, find a third point so that the three points form the vertices of an isosceles triangle.

Use a graphing utility to graph the equation.Use a standard setting.Approximate any intercepts. $y = 7 - \frac { 1 } { 2 } x$

Use the position equation s = -16t² + v₀t + s₀ to write a function that represents the situation and give the average velocity of the object from time t₁ to time t₂. An object is thrown upward from a height of 38 feet at a velocity of 84 feet per second. T₁ = 1, t₂ = 3

Let $f ( x ) = \frac { 1 } { x } , g ( x ) = x + 5$ .Find the composite function which expresses the given correspondence correctly. $\frac { 1 } { x + 5 }$

For following function, select (on the same set of coordinate axes) a graph for $c = - 3 , - 5 \text { and } - 1$ . $f ( x ) = \sqrt { x + c }$

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. $\left( - \frac { 1 } { 2 } , 5 \right)$

Find the graph of the equation. F (x) = | x - 2 |

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. $x = 2 , y = 58$

Select the graph of f and f^-1 on the same set of coordinate axes. F(x) = 2x - 3

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

Find $g \circ f$ and the domain of the composite function. $f ( x ) = x ^ { 2 } + 4 , g ( x ) = \sqrt { x }$

Find the difference quotient and simplify your answer. F(x) = x² - x + 1, $\frac { f ( 6 + h ) - f ( 6 ) } { h }$ , h $\neq$ 0