review the graph of function j(x). what is lim j(x)? x→3 3 4 5 6

Answer

Explanation:

Step1: Identify the relevant part of the graph.

We need to find the limit of $j(x)$ as $x$ approaches 3. We look at the behavior of the function (the red curve) around $x=3$.

Step2: Determine the limit from the left.

As $x$ approaches 3 from the left side (values less than 3), the graph of $j(x)$ approaches the y-value of the open circle on the red curve at $x=3$. $$ \lim_{x \to 3^-} j(x) = 4 $$

Step3: Determine the limit from the right.

As $x$ approaches 3 from the right side (values greater than 3), the graph of $j(x)$ approaches the y-value of the open circle on the red curve at $x=3$. $$ \lim_{x \to 3^+} j(x) = 4 $$

Step4: Conclude the overall limit.

Since the limit from the left and the limit from the right are equal, the limit of $j(x)$ as $x$ approaches 3 exists and is this common value. $$ \lim_{x \to 3} j(x) = 4 $$