### Home > APCALC > Chapter 2 > Lesson 2.1.1 > Problem2-14

2-14.

Let $f ( x ) = \left\{ \begin{array} { l l } { x ^ { 2 } - 1 } & { \text { for } x < 2 } \\ { 2 x + 3 } & { \text { for } x \geq 2 } \end{array} \right.$.

1. What is $f(2)$?

Notice the inequality symbols. $f(2)$ exists as part of the right side of $f(x)$ not the left.

$f(2) = 2(2)+3 = 7$

2. As $x \rightarrow 2^+, y \rightarrow$ ?

Compare this question to part (a).

3. As $x \rightarrow 2^−, y \rightarrow$ ?

Compare this question to part (a). Even though $f(2)$ does not exist in the left side of the equation, since both sides approach $x = 2$ we can evaluate what it approaches.

$x \rightarrow 2^−, y →(2)^2 − 1 \text{ or } y \rightarrow 3$

4. What do the results from parts (b) and (c) indicate about the graph?

Is $f(x)$ continuous at $x = 2$? In other words, does $f(x)$ approach the same $y$-value from the left and from the right of $x = 2$?