Chapter 12, Problem 1PS

a.

To determine

The graphs out of the given graphs that could be the graph of $f$ .

Answer to Problem 1PS

The graphs labeled $(i)$ and $(iv)$ could be the graph of $f$ for the given condition $\underset{x\to 2^{+}}{\lim }f(x)=3.$

Explanation of Solution

Given Information: Four graphs are given and condition of the function is: $\underset{x\to 2}{\lim }f(x)=3.$

Calculation:

From the given condition, when $x$ approaches $2$ , then $f(x)$ approaches $3$ .

Out of the given graphs, the graphs $(i)$ and $(iv)$ represent this condition.

So, the graphs labeled $(i)$ and $(iv)$ could be the graph of $f$ for the given condition $\underset{x\to 2^{+}}{\lim }f(x)=3.$

b.

To determine

The graphs out of the given graphs that could be the graph of $f$ .

Answer to Problem 1PS

The graphs labeled $(i)$ , $(iii)$ and $(iv)$ could be the graph of $f$ for the given condition $\underset{x\to 2^{+}}{\lim }f(x)=3.$

Explanation of Solution

Given Information: Four graphs are given and condition of the function is: $\underset{x\to 2^{-}}{\lim }f(x)=3.$

From the given condition, when $x$ approaches $2$ from the left hand side, then $f(x)$ approaches $3$ .

Out of the given graphs, the graphs $(i)$ , $(iii)$ and $(iv)$ represent this condition.

So, the graphs labeled $(i)$ , $(iii)$ and $(iv)$ could be the graph of $f$ for the given condition $\underset{x\to 2^{+}}{\lim }f(x)=3.$

c.

To determine

The graphs out of the given graphs that could be the graph of $f$ .

Answer to Problem 1PS

The graphs labeled $(i)$ and $(iv)$ could be the graph of $f$ for the given condition $\underset{x\to 2^{+}}{\lim }f(x)=3.$

Explanation of Solution

Given Information: Four graphs are given and condition of the function is: $\underset{x\to 2^{+}}{\lim }f(x)=3.$

Calculation:

From the given condition, when $x$ approaches $2$ from the right hand side, then $f(x)$ approaches $3$ .

Out of the given graphs, the graphs $(i)$ and $(iv)$ represent this condition.

So, the graphs labeled $(i)$ and $(iv)$ could be the graph of $f$ for the given condition $\underset{x\to 2^{+}}{\lim }f(x)=3.$