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Chapter 2: Problem 111

Use a graphing utility to graph each function. Use \(a[-5,5,1]\) by \([-5,5,1]\) viewing rectangle. Then find the intervals on which the function is increasing, decreasing, or constant. $$g(x)=\left|4-x^{2}\right|$$

Short Answer

Expert verified
Looking at the graph of the function, \(g(x)=\mid 4-x^{2}\mid\), it can be observed that the function is increasing on the interval \(-\infty < x < 0\) and decreasing on the interval \(0 < x < \infty\). There is no interval where it is constant.

Step by step solution

01

Graphing the function

On the graphing utility, input the function \(g(x)=\mid 4-x^{2}\mid \). Next, set the viewing rectangle with equal scales on the x and y-axis to give a clear view of the graph. Use the values \(x \in [-5,5]\) by \(y \in [-5,5]\). This will help to observe the function clearly.
02

Identifying the increasing and decreasing parts

Inspect the graph visually and identify the parts where the slope of the function is positive (increasing) and where it is negative (decreasing). Generally, observations could be as following: The function increases on the interval \(-\infty < x < 0\) and decreases on the interval \(0 < x < \infty\).
03

Identifying the constant function

A constant function is a function whose value doesn't change regardless of the input value. In this case, observing the graph, we see that there is no interval where the function is constant considering the function \(g(x)= \mid 4-x^{2}\mid\).

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