Amplitude, Vertical Shift, and Range

Front

What is Amplitude?

Back

Amplitude is the distance from the midline to the maximum or minimum value of a periodic function.

Front

What is a Vertical Shift?

Back

A vertical shift is a transformation that moves the graph of a function up or down without changing its shape.

Front

What is the Range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

What is another name for a Phase Shift?

Back

Horizontal Shift/Translation.

Front

What does a positive Amplitude indicate?

Back

A positive amplitude indicates that the graph oscillates above and below the midline.

Front

What does a negative Amplitude indicate?

Back

A negative amplitude indicates that the graph is reflected over the midline.

Front

How does a Vertical Shift affect the Range?

Back

A vertical shift changes the range of the function by adding or subtracting a constant value from all output values.

Front

What is the effect of a Horizontal Shift on the graph?

Back

A horizontal shift moves the graph left or right along the x-axis.

Front

What is the equation of a cosine function with an amplitude of 5 and a vertical shift of -3?

Back

y = 5 cos(x) - 3.

Front

How do you determine the maximum value of a function with a given amplitude and vertical shift?

Back

Maximum value = Vertical Shift + Amplitude.