Graph the function if the given changes are made in the indicated examples of this section. In

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Graph the function if the given changes are made in the indicated examples of this section.

In Example 3, if the coefficient of x is changed from 3 to 4, sketch the graph of the resulting function.


Data from Example 3

Sketch the graph of y = −2 cos 3x for 0 ≤ x ≤ 2π.

Note that the amplitude is 2 and the period is 2π/3. This means that one-fourth of the period is


Because the cosine curve is at a maximum or minimum for x = 0,
we find that y = −2 for x = 0 (the negative value is due to the minus sign before the
function), which means it is a minimum point. The curve then has a zero at x =π/6, a maximum value of 2 at


and its next value of



and so on. Therefore, we have the following table:


Using this table and the sinusoidal shape of the cosine curve, we sketch the function in Fig. 10.11.

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Basic Technical Mathematics

ISBN: 9780137529896

12th Edition

Authors: Allyn J. Washington, Richard Evans

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