Graphing Sine & Cosine with Transformations

Front

What is the general form of a cosine function with amplitude and vertical shift?

Back

f(x) = a cos(bx - c) + d, where |a| is the amplitude and d is the vertical shift.

Front

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

Back

The amplitude represents the maximum distance from the midline of the graph to its peak or trough.

Front

How do you determine the period of a cosine function?

Back

The period of a cosine function is given by the formula: Period = (2π)/|b|, where b is the coefficient of x.

Front

What is the effect of changing the value of 'b' in the function y = a cos(bx)?

Back

Changing 'b' affects the period of the function; a larger 'b' results in a shorter period.

Front

What is the phase shift in the function y = a sin(bx - c)?

Back

The phase shift is given by c/b, which indicates how much the graph is shifted horizontally.

Front

What is the vertical shift in the function y = a sin(bx) + d?

Back

The vertical shift is represented by 'd' and moves the entire graph up or down.

Front

How do you identify a horizontal shift in the function y = a sin(bx - c) + d?

Back

The horizontal shift is determined by the value of 'c'; if c is positive, the shift is to the right, and if negative, to the left.

Front

What is the amplitude of the function y = 4 cos(x) + 1?

Back

The amplitude is 4, which is the coefficient of the cosine function.

Front

What is the period of the function y = 2 sin(3x)?

Back

The period is (2π)/3, since b = 3.

Front

What does a negative amplitude indicate in a cosine function?

Back

A negative amplitude indicates a reflection of the graph across the midline.