# Bounded Exercises

### Example 1

Determine if the function is (a) bounded above or (b) bounded below.

*y*= cos*x*

### Example 2

Determine if the function is (a) bounded above or (b) bounded below.

*f*(*x*) = 5

### Example 3

Determine if the function is (a) bounded above (b) bounded below.

*f*(*x*) =*x*^{2}

### Example 4

Determine if the function is (a) bounded above or (b) bounded below.

*y*=*x*

### Example 5

Determine if the function is (a) bounded above or (b) bounded below.

### Example 6

Determine if the function is (a) bounded above or (b) bounded below.

### Example 7

Is the function is (a) bounded above or (b) bounded below?

### Example 8

Is the following function (a) bounded above or (b) bounded below?

### Example 9

Is the following function (a) bounded above or (b) bounded below?

### Example 10

Is the following statement true or false?

- If a function is bounded above it must also be bounded below.

### Example 11

Is the following statement true or false?

- If a function
*f*(*x*) has an upper bound of*M*there must be some value of*x*for which*f*(*x*) =*M*.

### Example 12

Is the following statement true or false?

- If there is some
*K*such that*f*(*x*) ≥*K*for all*x*, then the function*f*(*x*) is bounded below.