In the plane below, the blue graph represents y = sin x.

analyze the red graph and answer the following questions about the red graph:

1st question: the midline of the red graph is y =

2nd question: the amplitude of the red graph is =

3rd question: the equation of the red graph is=

ANSWER

a) y=-4

b) 2

c) y=2sinx-4

EXPLANATION

The midline divides the graph into two equal halves.

The midline of the red graph is

The amplitude is the distance from the midline to the peak of the graph.

The amplitude is 2.

The red graph is a transformation of the blue graph.

This transformation is of the form:

Where a=2 is the amplitude and d=4 is the downward shift by 4 units.