The graph of the function, given one value and the limit

[Emworthington]

Homework Statement

Sketch a graph of a function that satisfies the stated conditions:
lim f(x) [as x approaches 2) = 3 and f(2) = 4.

Homework Equations

N/A

The Attempt at a Solution

I know that the graph looks like an absolute value function (because the professor told me), but I'm really confused when I draw it out. As x approaches 2, the limit is 3. To me, this meant that the vertex of the graph is the coordinate (2,3) since 3 was the limit. However, when x=2, y=4, and the points can't coexist on this graph. What am I figuring/looking at wrong?

 

[SammyS]

Homework Statement

Sketch a graph of a function that satisfies the stated conditions:
lim f(x) [as x approaches 2) = 3 and f(2) = 4.

Homework Equations

N/A

The Attempt at a Solution

I know that the graph looks like an absolute value function (because the professor told me), but I'm really confused when I draw it out. As x approaches 2, the limit is 3. To me, this meant that the vertex of the graph is the coordinate (2,3) since 3 was the limit. However, when x=2, y=4, and the points can't coexist on this graph. What am I figuring/looking at wrong?

If this is the problem as given, it has nothing to do with an absolute value function.

It's a graph with a "hole" in it.