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# 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) = x2

### 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.
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