Math 1 · Unit 7 · Lesson 4 · part 3 of 6

End behavior: the far right and the far left

End behavior means: what does the graph do at the far right and the far left?

End behavior: the far right and the far left

End behavior means: what does the graph do at the far right and the far left? Say it plainly first, then in the math words.

Growth: y = 2 · 3^x

Plain: as x gets very big, y gets huge. As x goes far to the left, y gets close to 0.

Math words: as x goes to infinity, y goes to infinity. As x goes to negative infinity, y goes to 0.

The graph is increasing: it goes up everywhere from left to right.

Decay: y = 8 · 0.5^x

Plain: as x gets very big, y gets close to 0. As x goes far to the left, y gets huge.

Math words: as x goes to infinity, y goes to 0. As x goes to negative infinity, y goes to infinity.

The graph is decreasing: it goes down everywhere from left to right.

Zoom out on a decay curve and watch it hug the asymptote. The buttons widen the window; the curve keeps flattening toward y = 0 and never crosses it.

Increasing or decreasing is decided by b. b bigger than 1: increasing, and the curve climbs away from the asymptote on the right. b between 0 and 1: decreasing, and the curve settles toward the asymptote on the right. Either way the asymptote is y = 0 and the y-intercept is a.

Where to go next

Next: Read the features off a graphTwo curves. All the partsReading the Graph

End behavior: the far right and the far left