Graphs and Transformations of Trig Functions Flashcard

Front

What is the period of the function f(x) = 3 cos(4t) - 5?

Back

The period is π/2.

Front

What transformation of f(t) = sin(t) results in g(t) = sin(t) + 4?

Back

Vertical Translation.

Front

What is the amplitude of the function f(x) = 3 cos(4t) - 5?

Back

The amplitude is 3.

Front

What is the y-intercept of the function f(x) = 3 cos(4t) - 5?

Back

The y-intercept is (0, -2).

Front

What is the period of the graph of f(x) = cos(t)?

Back

The period is 2π.

Front

Define amplitude in the context of trigonometric functions.

Back

Amplitude is the maximum distance from the midline to the peak or trough of the graph.

Front

What is a vertical translation in the context of function transformations?

Back

A vertical translation shifts the graph up or down without changing its shape.

Front

How does a horizontal dilation affect the graph of a trigonometric function?

Back

A horizontal dilation stretches or compresses the graph along the x-axis.

Front

What is the effect of a negative coefficient in front of a cosine function?

Back

It reflects the graph across the x-axis.

Front

What is the general form of a sine function?

Back

f(t) = A sin(B(t - C)) + D, where A is amplitude, B affects period, C is horizontal shift, and D is vertical shift.