Question

sketch a possible graph of a function that satisfies the conditions below. determine whether f is continuous at x = 4. f(4)=3; lim┬(x→4)⁡f(x)=3 choose the correct graph below.

Explanation:

Step1: Recall continuity condition

A function $f(x)$ is continuous at $x = a$ if $\lim_{x
ightarrow a}f(x)=f(a)$. Here $a = 4$, $f(4)=3$ and $\lim_{x
ightarrow 4}f(x)=3$, so the function is continuous at $x = 4$.

Step2: Analyze graphs

For a continuous - function at $x = 4$, the graph should have no break, hole, or jump at $x = 4$. We need to look for a graph where the function value at $x = 4$ (the $y$ - value of the point on the graph when $x = 4$) is equal to the limit as $x$ approaches 4.

Answer:

We need to see the actual graphs to choose the correct one. But in general, the correct graph will be the one where there is a solid - point at $(4,3)$ and the function approaches $(4,3)$ as $x$ approaches 4 from both the left and the right. Without the ability to describe the individual graphs, we can't give a specific letter - answer. If you can describe the graphs in terms of the behavior at $x = 4$ (e.g., presence of holes, jumps, solid points), we can determine the correct choice.