Front

What is the amplitude in a sine or cosine function?

Back

The amplitude is the maximum distance from the midline of the graph to its peak or trough. It determines the height of the wave.

Front

What does the period of a sine or cosine function represent?

Back

The period is the distance along the x-axis for one complete cycle of the wave. It is calculated as 2π divided by the frequency.

Front

How does a vertical shift affect the graph of a function?

Back

A vertical shift moves the graph up or down without changing its shape. A positive shift moves it up, while a negative shift moves it down.

Front

What is a horizontal shift in graphing functions?

Back

A horizontal shift moves the graph left or right. A positive shift moves it to the right, while a negative shift moves it to the left.

Front

What is the general form of a sine function?

Back

The general form is y = A sin(B(x - C)) + D, where A is the amplitude, B affects the period, C is the horizontal shift, and D is the vertical shift.

Front

What is the general form of a cosine function?

Back

The general form is y = A cos(B(x - C)) + D, where A is the amplitude, B affects the period, C is the horizontal shift, and D is the vertical shift.

Front

If the amplitude is 4, what does this indicate about the graph?

Back

The graph will reach a maximum height of 4 units above the midline and a minimum height of 4 units below the midline.

Front

How do you determine the period of the function y = 4sin(½x)?

Back

The period is calculated as 2π divided by the coefficient of x, which is ½. Therefore, the period is 2π / (1/2) = 4π.

Front

What is the effect of changing the coefficient of x in a sine or cosine function?

Back

Changing the coefficient of x affects the period of the function. A larger coefficient results in a shorter period, while a smaller coefficient results in a longer period.

Front

What does a vertical shift of +3 mean for the function y = sin(x)?

Back

The graph of y = sin(x) will be moved up 3 units, shifting the midline from y = 0 to y = 3.