Trigonometry Graphing Trig Functions 3

Question 1

What is the range of y = 4sin(x) − 1?

Accepted Answer

[−5, 3]

Answer

Amplitude 4 gives [−4, 4] for the base, then shifting down 1 gives [−5, 3].

Question 2

Which equation has a graph with amplitude 3 and period π?

Accepted Answer

y = 3sin(2x)

Answer

Amplitude = 3 and period = 2π/2 = π, matching y = 3sin(2x).

Question 3

For y = cos(x − π/2), which familiar function does it equal?

Accepted Answer

sin(x)

Answer

cos(x − π/2) = sin(x) by the co-function shift identity.

Question 4

What is the x-intercept of y = sin(x) closest to x = π/2 (other than π/2 itself)?

Accepted Answer

x = π

Answer

The next x-intercept after π/2 is at x = π where sin(π) = 0.

Question 5

What does stretching y = sin(x) horizontally by a factor of 2 produce?

Accepted Answer

y = sin(x/2)

Answer

A horizontal stretch by factor 2 replaces x with x/2, giving y = sin(x/2).

Trigonometry Practice Test