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7-129.
  1. Find an equation for each graph below. Homework Help ✎

  2. a.

    b.

    c.

    d.

Use the general equation y = a · sin(xh) + k.
Determine the value for each of the three parameters.

First identify a convenient locator point.
In this case, we will use:

The x-value of the point represents the horizontal shift.
The y-value of the point represents the vertical shift.

The amplitude (a) is the distance from the midline (k) to the highest point.
In this case k = 2 and the highest point is 3, so a = 1.
Since the graph increases from the locator point in the same way y = sin x does, a is positive.

See part (a).
Pay careful attention to the scale on the y-axis when determining a and k.

notice the first cycle of the graph is an inverted sine curve, so the a value will be negative.

See part (a).

See parts (a) and (c).