Question

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 1

a) y=-4

b) 2

c) y=2sinx-4

Step-by-step explanation

The midline divides the graph into two equal halves.

The midline of the red graph is

`y = - 4`

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

`| - 2 - - 4| = 2`

The amplitude is 2.

The red graph is a transformation of the blue graph.

This transformation is of the form:

`y = a \sin(x) - d`

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

`y = 2\sin(x) - 4`