Limits and Graphs Examples

Given the graph of y = 3x² below, evaluate .

There is really only one thing to do here. We simply must make sure that the graph shows that the function approaches the same value from the left of x = 1 as it does from the right. Here, both sides approach y = 3. We can write our answer mathily as:

Given the graph of y = |x| below, evaluate  .

Once again, we must ensure that the graph approaches the same value from the left and the right. This is the case, as x = 0 is approached from the left and the right, the value of y approaches 0. That means the limit is 0.

Use the graph of the function f(x) to evaluate the given limits.

a) 

b) 

c) 

a) As was the case in Examples 1 and 2, we just need to examine the graph to see if the limits from the right and the left are equal. It does not matter what is actually happening at x = a. Here, both sides approach y = 3, so:

b) Does the graph approach the same values on the left and the right? No way José.

c) At x = c, the graph approaches y = 2 from the left and the right. Therefore, the limit as x approaches c is 2.