## Precalculus (6th Edition) Blitzer

A) $\underset{x\to 1}{\mathop{\lim }}\,f\left( x \right)=3$, since, as x approaches 1 the value of $f\left( x \right)$ gets closer to the y-coordinate of 3. B) The value of the function $f\left( 1 \right)$ is 2, thus $f\left( 1 \right)=2$ .
(a) Consider the provided limit $\underset{x\to 1}{\mathop{\lim }}\,f\left( x \right)$. To find $\underset{x\to 1}{\mathop{\lim }}\,f\left( x \right)$, examine the portion of the graph near $x=1$. As x approaches 1, the value of $f\left( x \right)$ gets closer to the y-coordinate of 3. This point $\left( 1,3 \right)$ is shown by the open dot in the above graph. The point $\left( 1,3 \right)$ has the y-coordinate of 3. Thus, $\underset{x\to 1}{\mathop{\lim }}\,f\left( x \right)=3$. Hence, the value of $\underset{x\to 1}{\mathop{\lim }}\,f\left( x \right)$ is 3. (b) Consider the provided function, $f\left( 1 \right)$. To find $f\left( 1 \right)$, examine the portion of the graph near $x=1$. The graph of the function ‘f’ at $x=1$ is shown by the open dot in the provided graph with coordinates $\left( 1,2 \right)$. Thus, $f\left( 1 \right)=2$.