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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=

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 th class=

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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

[tex]y = - 4[/tex]

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

[tex] | - 2 - - 4| = 2[/tex]

The amplitude is 2.

The red graph is a transformation of the blue graph.

This transformation is of the form:

[tex]y = a \sin(x) - d[/tex]

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

[tex]y = 2\sin(x) - 4[/tex]

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