# 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?