Question

use the graph of h in the given figure to find the following values or state that they do not exist. (a) h(2) (b) lim x→2 h(x) (c) h(7) (d) lim x→7 h(x) (e) lim x→8 h(x) (a) find h(2). select the correct choice and, if necessary, fill in the answer box to complete your choice. a. h(2)= (type an integer or a decimal.) b. h(2) is undefined.

Explanation:

Step1: Find h(2)

Look at the value of the function at x = 2 on the graph. There is a closed - circle at the point (2, 4), so h(2)=4.

Step2: Find $\lim_{x

ightarrow2}h(x)$
As x approaches 2 from both the left and the right, the function values approach 4. So $\lim_{x
ightarrow2}h(x)=4$.

Step3: Find h(7)

There is a closed - circle at the point (7, 2), so h(7)=2.

Step4: Find $\lim_{x

ightarrow7}h(x)$
As x approaches 7 from the left, the function values approach 2, and as x approaches 7 from the right, the function values approach 2. So $\lim_{x
ightarrow7}h(x)=2$.

Step5: Find $\lim_{x

ightarrow8}h(x)$
As x approaches 8 from the left, the function values approach - 2, and as x approaches 8 from the right, the function values approach - 2. So $\lim_{x
ightarrow8}h(x)=-2$.

Answer:

(a) h(2) = 4
(b) $\lim_{x
ightarrow2}h(x)=4$
(c) h(7) = 2
(d) $\lim_{x
ightarrow7}h(x)=2$
(e) $\lim_{x
ightarrow8}h(x)=-2$