Example 1
Is the following statement true or false?
- If f(x) is strictly increasing then f(x) must also be non-decreasing.
Example 2
Is the following statement true or false?
- If f(x) is non-increasing then f(x)must be strictly decreasing.
Example 3
Is the following statement true or false?
- The function f(x) must be at least one of the following: strictly increasing, non-decreasing, strictly decreasing, or non-increasing.
Example 4
Is the following function (a) strictly increasing, (b) non-decreasing, (c) strictly decreasing, (d) non-increasing, or (e) none of these? There may be more than one correct answer.
- y = 5
Example 5
Is the following function (a) strictly increasing, (b) non-decreasing, (c) strictly decreasing, (d) non-increasing, or (e) none of these options? There may be more than one correct answer.
- y = x2
Example 6
Is the following function (a) strictly increasing, (b) non-decreasing, (c) strictly decreasing, (d) non-increasing, or (e) none of these options? There may be more than one correct answer.
- y = x3
Example 7
Is the following function (a) strictly increasing, (b) non-decreasing, (c) strictly decreasing, (d) non-increasing, or (e) none of the above? There may be more than one correct answer.
- y = -x
Example 8
Consider the function f(x) graphed below.
What is the largest interval on which f(x) is
- strictly increasing?
Example 9
Consider the function f(x) graphed below.
What is the largest interval on which f(x) is
- non-decreasing?
Example 10
Consider the function f(x) graphed below.
What is the largest interval on which f(x) is
- strictly decreasing?
Example 11
Consider the function f(x) graphed below.
What's the largest interval where f(x) is non-increasing?