AP Calculus AB/BC 1.1 Limits
AP Calculus: Problem Explanation Limits Drill 1, Problem 1. Which of the following are true about the pictured function?
|MPAC 4||Connecting multiple representations|
Here are the potential answers...
OK, so we're given a graph and being tested on a few vocab words:
"Continuous"... "limit"... and "defined."
No short cuts here so we need to brute force and test each answer.
One... is the function continuous at point A?
Well, continuous means the function is defined at point A, and there's no hole in it.
From that hole and the actual point A, there's a pretty big jump...
...in other words, the function is NOT continuous at point A.
This is practically the textbook definition of DIScontinuous.
Ok check! One is true. So we can eliminate B, C, and E.
Two... does the function have a limit at point A?
Well, to find the limit at point A, the right and left limits of point A must exist... that
is, they aren't divided by zero... and have the same values.
But if we look at the graph, the right and left limits of point A clearly have different values.
...here... and here...
The values are some positive y-value and a negative y-value, so... different.
The function does NOT have a limit at point A. 2 is true, so check!
We don't even have to check number 3 because there's no I, II, and III option. So D's our answer.
But for you overachievers, let's take a look at 3.
Is the function defined at point A?
Well, yes it is; there's a filled point at point A. So 3 isn't true.
So D is our answer...done.