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Points, Vectors, and Functions

Points, Vectors, and Functions

Example 1

Exercises. Determine if each statement is true or false for a function f(x) defined on the whole real line. 

  • If f(x) is strictly increasing then f(x) must also be non-decreasing.

Example 2

Exercises. Determine if each statement is true or false for a function f(x) defined on the whole real line. 

  • If f(x) is non-increasing then f(x) must be strictly decreasing.

Example 3

Exercises. Determine if each statement is true or false for a function f(x) defined on the whole real line. 

  • The function f(x) must be at least one of the following: strictly increasing, non-decreasing, strictly decreasing, or non-increasing.

Example 4

Exercises. Determine whether each function is (a) strictly increasing, (b) non-decreasing, (c) strictly decreasing, (d) non-increasing, (e) none of the above. There may be more than one correct answer.

  • y = 5

Example 5

Exercises. Determine whether each function is (a) strictly increasing, (b) non-decreasing, (c) strictly decreasing, (d) non-increasing, (e) none of the above. There may be more than one correct answer.

  • y = x<sup>2</sup>

Example 6

Exercises. Determine whether each function is (a) strictly increasing, (b) non-decreasing, (c) strictly decreasing, (d) non-increasing, (e) none of the above. There may be more than one correct answer.

  • y = x<sup>3</sup>

Example 7

Exercises. Determine whether each function is (a) strictly increasing, (b) non-decreasing, (c) strictly decreasing, (d) non-increasing, (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. 

f(x) is

  • non-increasing?
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