Reading a Limit Off a Graph, Mark by Mark

You'll learnto trace a graph in from each side and read the height it is heading for, to tell an open circle from a solid dot and say which question each one answers, to report an estimate only as precisely as the grid supports, and to recognise the two ways a graph can refuse to have a limit at all.

A graph answers a limit question faster than algebra does, provided you ask it the right question. Put a finger on the curve to the left of the target and slide in; note the height you are heading for. Do the same from the right. If the two heights agree, that is the limit — and nothing drawn at the target itself has taken any part in the answer. The whole difficulty of this topic is that the mark at the target is the most visible thing on the page.

8 STEPS · 6 QUICK CHECKS · TRACE BOTH SIDES, THEN COMPARE · v1

trace in from each side, compare the two heights, and never read the mark at the target

Before you start

What you're looking at

One graph on a unit grid, with a target marked on the horizontal axis. An amber dot walks in along the curve from the left and a violet dot walks in from the right, and each drops a dashed line to the axis as it goes.

The question

What height is each side heading for — and once you have both, do they agree?

Watch for

A hollow ring marks a height the curve approaches. A solid disc marks a height the function actually takes. They are different shapes on purpose, and reading the disc when you were asked for the ring is the single most common error in this topic.

Step 1 / 8