Question

Asked May 17, 2019

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Consider the function g(x) = |(x^2 - 4)/(x+3)| do the following:

a) Give the domain of the function

b) find the peaks, valleys, and intercepts of the function.

Step 1

a) First obtain the singularity for the given function as follows.

The denominator of the given fraction is *x* + 3.

Thus, for *x* = –3 is the singularity point .

Then the given function is defined for all values of *x* except –3.

Therefore, the domain of the given function is

Step 2

b) From the graph shown below, peak is observed to be the local maximum point.

That is, the peak of the given function is at the point ( -0.76, 1.52).

Valley is a local minimum of the graph.

But here the valleys are at the points (-5.23,10.47), (-2,0) and (2,0).

Thus, the local minimum among those 3 points are (-2,0) and (2,0).

Step 3

Substitute *g*(x) = 0 in given equation to...

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