Use the figure below which gives a graph of the function fx

Use the figure below, which gives a graph of the function f(x), to give values for the indicated limits. (If any of the limits does not exist, enter the word none in the answer blank for that limit.)

(a) limx approaches ?2 f(x) =

(b) limx approaches 0 f(x) =

Please explain/show work

Solution

(a)

Find the left-hand limit:

What value does f(x) approach as x approaches 2 from the left?

f(x) approaches -2 as x approaches 2 from the left.

Therefore the limit as x approaches 2 from the left of f(x) is -2.

Find the right-hand limit:

What value does f(x) approach as x approaches 2 from the right?

f(x) approaches 9 as x approaches 2 from the right.

Therefore the limit as x approaches 2 from the right of f(x) is 9.

The left-hand limit does not equal the right-hand limit.

Therefore the limit as x approaches 2 of f(x) does not exist.

(b)

Find the left-hand limit:

What value does f(x) approach as x approaches 0 from the left?

f(x) approaches -6 as x approaches 0 from the left.

Therefore the limit as x approaches 0 from the left of f(x) is -6.

Find the right-hand limit:

What value does f(x) approach as x approaches 0 from the right?

f(x) approaches -6 as x approaches 0 from the right.

Therefore the limit as x approaches 0 from the right of f(x) is -6.

The left-hand limit equals the right-hand limit.

Therefore the limit as x approaches 0 of f(x) is -6.

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