Math 1 · Unit 2 · Lesson 4 · part 2 of 5
The checklist: five things to read off any graph
Lesson 3 read two things off a graph: how far left and right it goes (the domain, the inputs) and how far...
The checklist: five things to read off any graph
Lesson 3 read two things off a graph: how far left and right it goes (the domain, the inputs) and how far down and up (the range, the outputs). This lesson reads everything else. It is one checklist, and it works on any graph, even one with no formula behind it, like a temperature record or a story about a bike ride. The whole point is reading the picture, not working a formula.
- 1InterceptsWhere the graph crosses an axis. The x-intercept is where it crosses the x-axis: the output is 0 there. The y-intercept is where it crosses the y-axis: the input is 0 there, so it is the starting value. Say what each one means in the story.
- 2Increasing or decreasingRead left to right, like a sentence. Where the graph is climbing, it is increasing. Where it is falling, it is decreasing. Say where, with an inequality: increasing when 0 < x < 3.
- 3Positive or negativeWhere the graph is above the x-axis, the output is positive. Where it is below, the output is negative. Again say where: positive when 1 < x < 5.
- 4Maximum and minimumThe highest point is the maximum. The lowest is the minimum. Give both the input where it happens and the output value, when there is one.
- 5End behaviorWhat happens at the far ends, as the inputs get very big. Say it plainly first: as x keeps going to the right, the graph keeps climbing. Then name it: as x goes to infinity, y goes to infinity.
Increasing is not the same as positiveA graph can be climbing while it is still below the x-axis: increasing, but negative. It can be falling while it is above the axis: decreasing, but positive. Increasing and decreasing are about the direction you are moving. Positive and negative are about which side of the axis you are on. Keep the two pairs apart.