The function represents a <em>cosine</em> graph with axis at y = - 1, period of 6, and amplitude of 2.5.
<h3>How to analyze sinusoidal functions</h3>
In this question we have a <em>sinusoidal</em> function, of which we are supposed to find the following variables based on given picture:
Equation of the axis - Horizontal that represents the mean of the bounds of the function.
Period - Horizontal distance needed between two maxima or two minima.
Amplitude - Mean of the difference of the bounds of the function.
Type of sinusoidal function - The function represents either a sine or a cosine if and only if trigonometric function is continuous and bounded between - 1 and 1.
Then, we have the following results:
Equation of the axis: y = - 1
Period: 6
Amplitude: 2.5
The graph may be represented by a cosine with no <em>angular</em> phase and a sine with <em>angular</em> phase, based on the following trigonometric expression:
To find slope, use m=y2-y1/x2-x1, using values of x and y from two different points. Once you have found slope, take another point and use the point-slope equation y-y1=m(x-x1) and substitute in slope for m and the point for x1 and y1. Isolate y by subtracting y1 from both sides.
