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Points, Vectors, and Functions

Points, Vectors, and Functions

Increasing or Decreasing or... Exercises

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?

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