# 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

*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?