AnswersPrecalculusModeling with Trigonometric Expressions and Functions: Part Two

Practice Test Answers

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1
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What is the amplitude of the cosine function corresponding to the secant function graphed?

A
2
B
negative 1
C
negative 2
D
3
2
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Which of the following is the equation of the function shown in the graph?

A
y is equal to 0 point 5 secant open bracket 2 times open paren x plus pi close paren close bracket minus 4
B
y is equal to 2 cosecant open bracket 2 times open paren x plus pi close paren close bracket minus 2
C
y is equal to 0 point 5 cosecant open bracket 2 times open paren x plus pi close paren close bracket minus 4
D
y is equal to 2 secant open bracket 2 times open paren x plus pi close paren close bracket minus 2
3

What is the domain of the function y is equal to tangent of open paren x over 8 close paren ?

A
all real numbers except 4 pi plus 4 n pi , where n is any integer
B
all real numbers except 8 pi plus 4 n pi , where n is any integer
C
all real numbers except 8 pi plus 8 n pi , where n is any integer
D
all real numbers except 4 pi plus 8 n pi , where n is any integer
4

Which of the following is the graph of y is equal to sine of open paren 4 times open paren x minus pi close paren close paren ?

A
Image with description A coordinate plane. The graph starts and rises to (0 comma 1). It falls through (pi over 8 comma negative 1) to (pi over 4 comma negative 3). It then rises through (3 pi over 8 comma negative 1) to (pi over 2 comma 1). It then falls through (5 pi over 8 comma negative 1) to (3 pi over 4 comma negative 3). It then rises through (7 pi over 8 comma negative 1) to (pi comma 1). It then falls through (9 pi over 8 comma negative 1) to (5 pi over 4 comma negative 3). It then rises through (11 pi over 8 comma negative 1) to (3 pi over 2 comma 1). It then falls through (13 pi over 8 comma negative 1) to (7 pi over 4 comma negative 3). It then rises through (15 pi over 8 comma negative 1) to (2 pi comma 1).
B
Image with description A coordinate plane. The graph starts and rises to (negative 4 pi comma 1). It starts to fall through (negative 3 pi comma 0) to (negative 2 pi comma negative 1). It then rises through (negative pi comma 0) to (0 comma 1). It then falls through (pi comma 0) to (2 pi comma negative 1). It then rises through (3 pi comma 0) to (4 pi comma 1).
C
Image with description A coordinate plane. The graph starts and falls to (negative pi comma negative 3). It rises through (negative 3 pi over 4 comma negative 1) to (negative pi over 2 comma 1). It then falls through (negative pi over 4 comma negative 1) to (0 comma negative 3). It then rises through (pi over 4 comma negative 1) to (pi over 2 comma 1). It then falls through (3 pi over 4 comma negative 1) to (pi comma negative 3).
D
Image with description A coordinate plane. The graph starts and rises to (negative 2 pi comma 1). It starts to fall through (negative 7 pi over 4 comma 0) to (negative 3 pi over 2 comma negative 1). It then rises through (negative 5 pi over 4 comma 0) to (negative pi comma 1). It then falls through (negative 3 pi over 4 comma 0) to (negative pi over 2 comma negative 1). It then rises through (negative pi over 4 comma 0) to (0 comma 1). It then falls through (pi over 4 comma 0) to (pi over 2 comma negative 1). It then rises through (3 pi over 4 comma 0) to (pi comma 1). It then falls through (5 pi over 4 comma 0) to (3 pi over 2 comma negative 1). It then rises through (7 pi over 4 comma 0) to (2 pi comma 1).
5

What restriction should be applied to y is equal to tangent x for y is equal to arctan x to be defined?

A
restrict the domain to left bracket negative pi over 2 comma pi over 2 right bracket
B
restrict the domain to open paren negative pi over 2 comma pi over 2 close paren
C
restrict the range to open paren negative pi over 2 comma pi over 2 close paren
D
restrict the range to left bracket negative pi over 2 comma pi over 2 right bracket
6

A student uses the equation tangent theta is equal to the fraction with numerator s squared and denominator 49 to represent the speed, s , in feet per second, of a toy car driving around a circular track having an angle of incline theta , where sine theta is equal to 1 half To solve the problem, the student used the given value of sine theta to find the value of tangent theta and then substituted the value of tangent theta in the equation above to solve for s What is the approximate value of s , the speed of the car in feet per second?

A
5 point 3
B
28 point 3
C
9 point 2
D
7 point 5
7

Which point does the graph of the parent function y is equal to tangent of x pass through?

A
open paren pi over 3 comma square root of 3 close paren
B
open paren pi over 3 comma the fraction with numerator square root of 3 and denominator 3 close paren
C
open paren square root of 3 comma pi over 3 close paren
D
open paren the fraction with numerator square root of 3 and denominator 3 comma pi over 3 close paren
8

Which graph represents the inverse of the function in this graph?

A
Image with description On a coordinate plane, a function approaches x = negative StartFraction pi Over 2 EndFraction in quadrant 3, has an inflection point at (0, 0), and approaches x = StartFraction pi Over 2 EndFraction in quadrant 1.
B
Image with description On a coordinate plane, a function approaches x = negative StartFraction pi Over 2 EndFraction in quadrant 2, has an inflection point at (0, 0), and approaches x = StartFraction pi Over 2 EndFraction in quadrant 4.
C
Image with description On a coordinate plane, a function approaches y = negative StartFraction pi Over 2 EndFraction in quadrant 4, increases through an inflection point at (0, 0), and approaches y = StartFraction pi over 2 EndFraction in quadrant 2.
D
Image with description On a coordinate plane, a function approaches y = negative StartFraction pi Over 2 EndFraction in quadrant 3, increases through an inflection point at (0, 0), and approaches y = StartFraction pi over 2 EndFraction in quadrant 1.
9

If a vertical line is dropped from the x -axis to the point open paren 12 comma negative 9 close paren in the diagram, what is the value of secant theta ?

A
5 fourths
B
negative 5 thirds
C
negative 5 fourths
D
5 thirds
10

Which transformations are needed to change the parent sine function to the sine function shown in the graph?

A
vertical stretch of 2 , horizontal compression to a period of 4 pi , vertical shift of 2 units up, phase shift of pi units left
B
vertical stretch of 1 half , horizontal compression to a period of 2 pi , vertical shift of 1 unit up, phase shift of pi units left
C
vertical compression of 1 half , horizontal stretch to a period of 2 pi , vertical shift of 1 unit down, phase shift of pi units left
D
vertical compression of 1 half , horizontal stretch to a period of 4 pi , vertical shift of 1 unit up, phase shift of pi units left

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