Graph Transformations and Parameters

The video tutorial explains how parameters a, b, c, and d affect sinusoidal functions. Parameters a and c, located outside the function, influence the vertical direction, affecting amplitude and vertical shifts. Parameters b and d, inside the function, impact the horizontal direction, altering the period and phase displacement. The tutorial details how these parameters cause the graph to stretch, compress, shift, and reflect, providing a comprehensive understanding of their roles in graph transformations.

Which parameters affect the vertical direction of the graph?

• a and b

• b and d

• a and c

• c and d

What happens to the graph when parameter c is increased?

• It shifts left

• It shifts right

• It shifts down

• It shifts up

How does parameter d affect the graph?

• It affects the period

• It changes the phase displacement

• It shifts the graph vertically

• It changes the amplitude

What is the effect of subtracting a value from x in the function?

• Increases amplitude

• Decreases amplitude

• Shifts the graph left

• Shifts the graph right

What role does parameter a play in the graph's transformation?

• It alters the amplitude

• It changes the phase displacement

• It shifts the graph horizontally

• It affects the period

If a is less than zero, what happens to the graph?

• It shifts up

• It reflects across the sinusoidal axis

• It becomes narrower

• It becomes wider

How does parameter b affect the period of the graph?

• It has no effect

• It doubles the period

• It halves the period

• It is inversely proportional to the period

What happens to the graph when b is greater than 1?

• The graph shifts down

• The graph shifts up

• The graph becomes narrower

• The graph becomes wider

Which parameter is responsible for the phase displacement?

• c

• b

• a

• d

What is the general effect of parameters inside the function?

• They only affect the amplitude

• They affect the vertical direction

• They affect the horizontal direction

• They have no effect