About Increasing, Decreasing, and Constant Intervals:

We will sometimes have to determine where a function is increasing, decreasing, or constant by inspecting its graph. We normally say that a function is increasing on some interval of its domain if f(a) is greater than f(b) for all a, b in that interval such that a is greater than b. Additionally, we can say that a function is decreasing on some interval of its domain if f(a) is less than f(b) for all a, b in that interval such that a is greater than b.

Test Objectives
  • Demonstrate the ability to find the intervals where a function is increasing, decreasing, or constant
Increasing, Decreasing, and Constant Intervals Practice Test:

#1:

Instructions: find the intervals where the function is increasing, decreasing, or constant.

$$a)\hspace{.2em}$$

Graphing the function f(x)=-x^2 - 6x - 4

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#2:

Instructions: find the intervals where the function is increasing, decreasing, or constant.

$$a)\hspace{.2em}$$

Graphing the function |x - 2| + 1

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#3:

Instructions: find the intervals where the function is increasing, decreasing, or constant.

$$a)\hspace{.2em}$$

Graphing the function

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#4:

Instructions: find the intervals where the function is increasing, decreasing, or constant.

$$a)\hspace{.2em}$$

Graphing the function

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#5:

Instructions: find the intervals where the function is increasing, decreasing, or constant.

$$a)\hspace{.2em}$$

Graphing the function

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Written Solutions:

#1:

Solutions:

$$a)\hspace{.2em}$$ $$\text{Increasing on:}\hspace{.2em}(-\infty, -5)$$ $$\text{Decreasing on:}\hspace{.2em}(-5, \infty)$$

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#2:

Solutions:

$$a)\hspace{.2em}$$ $$\text{Increasing on:}\hspace{.2em}(1, \infty)$$ $$\text{Decreasing on:}\hspace{.2em}(-\infty, 1)$$

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#3:

Solutions:

$$a)\hspace{.2em}$$ $$\text{Increasing on:}\hspace{.2em}(-1,1)$$ $$\text{Decreasing on:}\hspace{.2em}(-\infty, -1),(1,\infty)$$

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#4:

Solutions:

$$a)\hspace{.2em}$$ $$\text{Increasing on:}\hspace{.2em}(-\infty, \infty)$$

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#5:

Solutions:

$$a)\hspace{.2em}$$ $$\text{Increasing on:}\hspace{.2em}(-4, 0), (4, \infty)$$ $$\text{Decreasing on:}\hspace{.2em}(-\infty, -4), (0, 4)$$

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