Math 1 · Unit 2 · Lesson 4 · part 3 of 5
The checklist on one graph, all the way through
Here is the checklist run all the way through on a curve.
The checklist on one graph, all the way through
Here is the checklist run all the way through on a curve. A ball is tossed from a hole in the ground; the graph shows its height above the ground (y, in feet) against time (x, in seconds). Nobody is asking you for a formula. Just read.
1. Interceptsx-intercepts at x = 1 and x = 5: the output is 0, the ball is at ground level. It comes up out of the hole at 1 second and falls back in at 5. y-intercept at (0, −5): the input is 0, so at the start the ball is 5 feet below ground.
2. Increasing, decreasingClimbing when x < 3 (increasing). Falling when x > 3 (decreasing). The ball rises for 3 seconds, then falls.
3. Positive, negativeAbove the x-axis when 1 < x < 5: positive, the ball is above ground. Below the axis when x < 1 or x > 5: negative, the ball is in the hole.
4. Maximum, minimumMaximum at (3, 4): the highest point, 4 feet up, at 3 seconds. No minimum on this graph: it keeps going down at both ends.
5. End behaviorAs x keeps going to the right, the graph keeps falling. As x goes to infinity, y goes to negative infinity. (In the story, the ball would stop at the bottom of the hole; the curve does not know that.)
Notice that between x = 1 and x = 3 the graph is both increasing and positive, and between x = 3 and x = 5 it is decreasing but still positive. The two pairs of words really are different questions.