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Section 1.4 Increasing and Decreasing

In this section, we will look at graphs to determine where a function is increasing or decreasing. We will also learn how to identify the intervals where a function is increasing or decreasing.

Exercises Read-Watch-Try

1.

The graph of the function \(g(x)\) is shown below. On what interval or intervals is \(g(x)\) increasing?
  • \((1, \infty)\)
  • \((-\infty, 1)\)
  • \([1, \infty)\)
  • \((-\infty, 1]\)

2.

The graph of the function \(g(x)\) is shown below. On what interval or intervals is \(g(x)\) decreasing?
  • \((1, \infty)\)
  • \((-\infty, 1)\)
  • \([1, \infty)\)
  • \((-\infty, 1]\)

3.

The graph of the function \(f(x)\) is shown below. On what interval or intervals is \(g(x)\) increasing?
  • \((-\infty, -2)\)
  • \((-\infty, -2)\cup(2,\infty)\)
  • \((2, \infty)\)
  • \((-2, 2)\)

4.

The graph of the function \(f(x)\) is shown below. On what interval or intervals is \(g(x)\) decreasing?
  • \((-\infty, -2)\)
  • \((-\infty, -2)\cup(2,\infty)\)
  • \((2, \infty)\)
  • \((-2, 2)\)