# 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*=*x*^{2}

### 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*=*x*^{3}

### 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?