Question 1

Which of the following is a solution to the given equation? ​   ​

Accepted Answer

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

Question 2

Which set of ordered pairs represents a function from P to Q? P = {5, 10, 15, 20} Q = {-1, 1, 3}
​

Accepted Answer

A) {(5, 3), (15, 1), (5, -1), (15, 3)} 
B) {(15, -1), (15, 1), (15, 3)} 
C) {(5, -1), (10, 1), (10, 3), (15, 1), (20, -1)} 
D) {(15, 1), (10, -1), (5, 1), (10, 3), (15, -1)} 
E) {(5, -1), (10, 1), (15, 3), (20, -1)} 
A) {(5, 3), (15, 1), (5, -1), (15, 3)} 
B) {(15, -1), (15, 1), (15, 3)} 
C) {(5, -1), (10, 1), (10, 3), (15, 1), (20, -1)} 
D) {(15, 1), (10, -1), (5, 1), (10, 3), (15, -1)} 
E) {(5, -1), (10, 1), (15, 3), (20, -1)}

Question 3

Give a verbal description of the subset of real numbers represented by the following inequality, and sketch the subset on the real number line. ​
​-3 ≤ x < 0
​

Accepted Answer

A) ​-3 ≤ x < 0 denotes the set of all real numbers greater than or equal to -3 and less than or equal to 0.   
B) ​-3 ≤ x < 0 denotes the set of all real numbers greater than or equal to -3 and less than 0.   
C) ​-3 ≤ x < 0 denotes the set of all real numbers greater than or equal to -3 and less than 0.   
D) ​-3 ≤ x < 0 denotes the set of all real numbers greater than or equal to -3 and less than 0.   
E) ​-3 ≤ x < 0 denotes the set of all real numbers less than or equal to -3 and greater than 0.   
A) ​-3 ≤ x < 0 denotes the set of all real numbers greater than or equal to -3 and less than or equal to 0.   
B) ​-3 ≤ x < 0 denotes the set of all real numbers greater than or equal to -3 and less than 0.   
C) ​-3 ≤ x < 0 denotes the set of all real numbers greater than or equal to -3 and less than 0.   
D) ​-3 ≤ x < 0 denotes the set of all real numbers greater than or equal to -3 and less than 0.   
E) ​-3 ≤ x < 0 denotes the set of all real numbers less than or equal to -3 and greater than 0.

Question 4

Use the graph of   to write an equation for the function whose graph is shown. ​
​   ​

Accepted Answer

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

Question 5

Reduce the index of the radical.   ​

Accepted Answer

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

Question 6

Identify the parent function and the transformation shown in the graph.Write an equation for the function shown in the graph. ​   ​

Accepted Answer

A) Reflection in the y-axis and vertical shrink of   . 
B) Reflection in the y-axis and vertical shrink of   . 
C) Reflection in the y-axis and vertical shrink of   . 
D) Reflection in the y-axis and vertical shrink of   . 
E) Reflection in the y-axis and vertical shrink of   . 
A) Reflection in the y-axis and vertical shrink of   . 
B) Reflection in the y-axis and vertical shrink of   . 
C) Reflection in the y-axis and vertical shrink of   . 
D) Reflection in the y-axis and vertical shrink of   . 
E) Reflection in the y-axis and vertical shrink of   .

Question 7

Use a graphing utility to graph the function and approximate (to two decimal places) any relative minimum or relative maximum values.

Accepted Answer

A) relative maximum: (2.58, 0.39) relative minimum: (7.27, -1.72) 
B) relative maximum: (0.39, 2.58) relative minimum: (-1.72, 7.27) 
C) relative maximum: (-1.72, 7.27) relative minimum: (0.39, 2.58) 
D) relative maximum: (7.27, -1.72) relative minimum: (2.58, 0.39) 
E) relative maximum: (2.58, 28.33) relative minimum: (7.27, 478.41) 
A) relative maximum: (2.58, 0.39) relative minimum: (7.27, -1.72) 
B) relative maximum: (0.39, 2.58) relative minimum: (-1.72, 7.27) 
C) relative maximum: (-1.72, 7.27) relative minimum: (0.39, 2.58) 
D) relative maximum: (7.27, -1.72) relative minimum: (2.58, 0.39) 
E) relative maximum: (2.58, 28.33) relative minimum: (7.27, 478.41)

Question 8

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 9

An object is dropped from a height of 60 feet. Use the position equation s = -16t2 + v0t + s0 to write a function that represents the situation and select the graph of the function.
​

Accepted Answer

A) s = 16t2 + ​60 ​
​   
B) s = -16t2 - ​60 ​
​   
C) s = 16t2 - ​60 ​
​   
D) s = -16t2 + ​60 ​
​   
E) s = -16t2 + ​60t ​
​   
A) s = 16t2 + ​60 ​
​   
B) s = -16t2 - ​60 ​
​   
C) s = 16t2 - ​60 ​
​   
D) s = -16t2 + ​60 ​
​   
E) s = -16t2 + ​60t ​
​

Question 10

Select the graph of the given function and determine the interval(s) for which f(x) ≥ 0. ​   ​

Accepted Answer

A) ​   ​
(-∞, 2] 
B) ​   ​
[-2, ∞) 
C) ​   ​
​[-2, 2) 
D) ​   ​
[2, ∞) 
E) ​   ​
[-2, ∞) 
A) ​   ​
(-∞, 2] 
B) ​   ​
[-2, ∞) 
C) ​   ​
​[-2, 2) 
D) ​   ​
[2, ∞) 
E) ​   ​
[-2, ∞)

Question 11

Identify the parent function and the transformation shown in the graph.Write an equation for the function shown in the graph. ​   ​

Accepted Answer

A) Reflection in the x-axis of   
B) Horizontal shift of x-axis of   
C) Reflection in the y-axis of   
D) Horizontal shift of x-axis of   
E) Reflection in the y-axis of   
A) Reflection in the x-axis of   
B) Horizontal shift of x-axis of   
C) Reflection in the y-axis of   
D) Horizontal shift of x-axis of   
E) Reflection in the y-axis of

Question 12

Write the number in decimal notation. ​
- 5)718 × 10-3
​

Accepted Answer

A) - 0.005718 
B) 0.5718 
C) - 0.05718 
D) 0.005718 
E) - 0.0005718 
A) - 0.005718 
B) 0.5718 
C) - 0.05718 
D) 0.005718 
E) - 0.0005718

Question 13

Let   .Find the composite function which expresses the given correspondence correctly. ​   ​

Accepted Answer

A)    
B)    
C)    
D)    
E) none of the above 
A)    
B)    
C)    
D)    
E) none of the above

Question 14

Write the number in scientific notation. ​- 0.000375​
​

Accepted Answer

A) - 3.75 × 10-4 
B) - 3.75 × 102 
C) 3.75 × 103 
D) - 0.000375 × 104 
E) 0.000375 × 102 
A) - 3.75 × 10-4 
B) - 3.75 × 102 
C) 3.75 × 103 
D) - 0.000375 × 104 
E) 0.000375 × 102

Question 15

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

Accepted Answer

A) -7 
B)    
C) 7 
D) 2x + 7 
E) 2 
A) -7 
B)    
C) 7 
D) 2x + 7 
E) 2

Question 16

Fill in the missing form of the expression. ​
Radical Form Rational Exponent Form   -------
​

Accepted Answer

A)    ​ 
B) 6.5 
C)    ​ 
D)    
E)    
A)    ​ 
B) 6.5 
C)    ​ 
D)    
E)

Question 17

Evaluate ​f(16) if   .​

Accepted Answer

A) ​f(16) = 5 
B) ​f(16) = 7 
C) ​f(16) = 4 
D) ​f(16) = 8 
E) ​f(16) = 6 
A) ​f(16) = 5 
B) ​f(16) = 7 
C) ​f(16) = 4 
D) ​f(16) = 8 
E) ​f(16) = 6

Question 18

For following function, select (on the same set of coordinate axes) a graph for   . ​   ​

Accepted Answer

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

Question 19

Write the standard form of the equation of the circle with the given characteristics. center: (-5, -4); solution point: (-3, -7)

Accepted Answer

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

Question 20

A pebble is dropped into a calm pond, causing ripples in the form of concentric circles.The radius (in feet) of the outer ripple is   , where t is the time in seconds after the pebble strikes the water.The area of the circle is given by the function   .Find and interpret   . ​

Accepted Answer

A)    ;   represents the area of the circle at time t. 
B)    ;   represents the area of the circle at time t. 
C)    ;   represents the area of the circle at time t. 
D)    ;   represents the area of the circle at time t. 
E)    ;   represents the area of the circle at time t. 
A)    ;   represents the area of the circle at time t. 
B)    ;   represents the area of the circle at time t. 
C)    ;   represents the area of the circle at time t. 
D)    ;   represents the area of the circle at time t. 
E)    ;   represents the area of the circle at time t.

Which of the following is a solution to the given equation?

Which set of ordered pairs represents a function from P to Q? P = {5, 10, 15, 20} Q = {-1, 1, 3}

Give a verbal description of the subset of real numbers represented by the following inequality, and sketch the subset on the real number line. -3 ≤ x < 0

Use the graph of to write an equation for the function whose graph is shown.

Reduce the index of the radical.

Identify the parent function and the transformation shown in the graph.Write an equation for the function shown in the graph.

Use a graphing utility to graph the function and approximate (to two decimal places) any relative minimum or relative maximum values.

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

An object is dropped from a height of 60 feet. Use the position equation s = -16t² + v₀t + s₀ to write a function that represents the situation and select the graph of the function.

Select the graph of the given function and determine the interval(s) for which f(x) ≥ 0.

Identify the parent function and the transformation shown in the graph.Write an equation for the function shown in the graph.

Write the number in decimal notation. - 5)718 × 10^-3

Let .Find the composite function which expresses the given correspondence correctly.

Write the number in scientific notation. - 0.000375

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

Fill in the missing form of the expression. Radical Form Rational Exponent Form -------

Evaluate f(16) if .

For following function, select (on the same set of coordinate axes) a graph for .

Write the standard form of the equation of the circle with the given characteristics. center: (-5, -4); solution point: (-3, -7)

A pebble is dropped into a calm pond, causing ripples in the form of concentric circles.The radius (in feet) of the outer ripple is , where t is the time in seconds after the pebble strikes the water.The area of the circle is given by the function .Find and interpret .

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Exam 7: Prerequisites

Which of the following is a solution to the given equation? ​ ​

Which set of ordered pairs represents a function from P to Q? P = {5, 10, 15, 20} Q = {-1, 1, 3} ​

Give a verbal description of the subset of real numbers represented by the following inequality, and sketch the subset on the real number line. ​ ​-3 ≤ x < 0 ​

Use the graph of to write an equation for the function whose graph is shown. ​ ​ ​

Reduce the index of the radical. ​

Identify the parent function and the transformation shown in the graph.Write an equation for the function shown in the graph. ​ ​

Use a graphing utility to graph the function and approximate (to two decimal places) any relative minimum or relative maximum values.

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

An object is dropped from a height of 60 feet. Use the position equation s = -16t2 + v0t + s0 to write a function that represents the situation and select the graph of the function. ​

Select the graph of the given function and determine the interval(s) for which f(x) ≥ 0. ​ ​

Identify the parent function and the transformation shown in the graph.Write an equation for the function shown in the graph. ​ ​

Write the number in decimal notation. ​ - 5)718 × 10-3 ​

Let .Find the composite function which expresses the given correspondence correctly. ​ ​

Write the number in scientific notation. ​- 0.000375​ ​

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

Fill in the missing form of the expression. ​ Radical Form Rational Exponent Form ------- ​

Evaluate ​f(16) if .​

For following function, select (on the same set of coordinate axes) a graph for . ​ ​

Write the standard form of the equation of the circle with the given characteristics. center: (-5, -4); solution point: (-3, -7)

A pebble is dropped into a calm pond, causing ripples in the form of concentric circles.The radius (in feet) of the outer ripple is , where t is the time in seconds after the pebble strikes the water.The area of the circle is given by the function .Find and interpret . ​

Trigonometry

Analytic-Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

Filters

Which of the following is a solution to the given equation?

Which set of ordered pairs represents a function from P to Q? P = {5, 10, 15, 20} Q = {-1, 1, 3}

Give a verbal description of the subset of real numbers represented by the following inequality, and sketch the subset on the real number line. -3 ≤ x < 0

Use the graph of to write an equation for the function whose graph is shown.

Reduce the index of the radical.

Identify the parent function and the transformation shown in the graph.Write an equation for the function shown in the graph.

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

An object is dropped from a height of 60 feet. Use the position equation s = -16t² + v₀t + s₀ to write a function that represents the situation and select the graph of the function.

Select the graph of the given function and determine the interval(s) for which f(x) ≥ 0.

Identify the parent function and the transformation shown in the graph.Write an equation for the function shown in the graph.

Write the number in decimal notation. - 5)718 × 10^-3

Let .Find the composite function which expresses the given correspondence correctly.

Write the number in scientific notation. - 0.000375

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

Fill in the missing form of the expression. Radical Form Rational Exponent Form -------

Evaluate f(16) if .

For following function, select (on the same set of coordinate axes) a graph for .

A pebble is dropped into a calm pond, causing ripples in the form of concentric circles.The radius (in feet) of the outer ripple is , where t is the time in seconds after the pebble strikes the water.The area of the circle is given by the function .Find and interpret .