Question

use the graph of g(x) to evaluate (lim_{x \to 5^+} g(x)) (options: ( infty ), does not exist, ( -3 ), ( 1 ))

Explanation:

Step1: Understand Right-Hand Limit

The right - hand limit $\lim_{x
ightarrow a^{+}}g(x)$ is the value that $g(x)$ approaches as $x$ gets closer to $a$ from the right - hand side (values of $x$ greater than $a$).

Step2: Analyze the Graph for $x

ightarrow5^{+}$
From the graph, as $x$ approaches $5$ from the right (moving along the $x$ - axis towards $5$ from values like $5.1,5.01,5.001,\cdots$), we observe the behavior of the function $g(x)$. The graph shows that as $x$ approaches $5$ from the right, the function values seem to approach a specific finite value. Looking at the points and the trend of the graph (the open circles and the direction of the graph as $x$ approaches $5$ from the right), we can see that the function approaches $1$.

Answer:

1 (corresponding to the teal - colored option with value 1)