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
#1:
Instructions: find the intervals where the function is increasing, decreasing, or constant.
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#2:
Instructions: find the intervals where the function is increasing, decreasing, or constant.
$$a)\hspace{.2em}$$
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#3:
Instructions: find the intervals where the function is increasing, decreasing, or constant.
$$a)\hspace{.2em}$$
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#4:
Instructions: find the intervals where the function is increasing, decreasing, or constant.
$$a)\hspace{.2em}$$
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#5:
Instructions: find the intervals where the function is increasing, decreasing, or constant.
$$a)\hspace{.2em}$$
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Written Solutions:
#1:
Solutions:
$$a)\hspace{.2em}$$ $$\text{Increasing on:}$$ $$(-\infty, -5)$$ $$\text{Decreasing on:}$$ $$(-5, \infty)$$
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#2:
Solutions:
$$a)\hspace{.2em}$$ $$\text{Increasing on:}$$ $$(1, \infty)$$ $$\text{Decreasing on:}$$ $$(-\infty, -1)$$ $$\text{Constant on:}$$ $$(-1, 1)$$
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#3:
Solutions:
$$a)\hspace{.2em}$$ $$\text{Increasing on:}$$ $$(-1,1)$$ $$\text{Decreasing on:}$$ $$(-\infty, -1) \hspace{.1em}\text{and}\hspace{.1em}(1,\infty)$$
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#4:
Solutions:
$$a)\hspace{.2em}$$ $$\text{Increasing on:}$$ $$(-\infty, \infty)$$
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#5:
Solutions:
$$a)\hspace{.2em}$$ $$\text{Increasing on:}$$ $$(-4, 0) \hspace{.1em}\text{and}\hspace{.1em}(4, \infty)$$ $$\text{Decreasing on:}$$$$(-\infty, -4) \hspace{.1em}\text{and}\hspace{.1em}(0, 4)$$
