Math 1 · Unit 7 · Lesson 4

Reading the Graph

Every feature of an exponential graph comes from a or b. It crosses the y-axis at a. Its domain is all real numbers. Its range is y greater than 0, because positive times positive stays positive. It gets closer and closer to the x-axis without ever touching it: the horizontal asymptote y = 0. End behavior says what happens far right and far left, plainly first and then in math words. Then match equations to graphs by elimination: direction from b, crossing from a.

About 45 minutes Closer and closer, never touching

The big idea

Every feature of the exponential graph traces back to a or b. The y-intercept is (0, a) because b to the zero is 1. The domain is all real numbers because the table walks both ways forever. The range is y greater than 0 because a positive start multiplied by positive factors stays positive; it can shrink toward 0 but never reach it, so the x-axis y = 0 is a horizontal asymptote, a line the curve approaches without touching. End behavior says what happens at the far right and far left: plainly, y gets huge or gets close to 0; in math words, as x goes to infinity or negative infinity. Growth curves increase and decay curves decrease, decided by b. To match an equation to its graph, read the direction from b, then the crossing from a, and cross out everything that breaks a rule.

The parts of this lesson

Each part is its own short page. Go in order, or pick the one you need.

1The Words We UseThe vocabulary for this lesson, in one place.Start here 2Four key features, and where each comes fromIn Unit 3, Lesson 3 you learned to read a line's graph: where it crosses, which way it tilts. 3End behavior: the far right and the far leftEnd behavior means: what does the graph do at the far right and the far left? 4Read the features off a graphTwo curves. 5Match the equation to its graph, by eliminationSame test-day habit as Unit 3, Lesson 3: do not plug in points. 6Practice ProblemsTry them, get help one step at a time, then print how it went.

Printables

One page with the four key features and their reasons, the asymptote picture, end behavior in both languages, and the two-look matching habit. Plus a worksheet with an answer key and a short lesson plan.

Study guide (PDF) Worksheet and answer key (PDF) Lesson plan (PDF)

Where this goes next

Previous lesson: Growth and DecayWhat b decides, and percents. Next lesson: Linear or Exponential?Telling the two families apart from a table, a story, or a graph. Back to the Math 1 mapEvery Math 1 lesson, in course order. Tell us what you thoughtA few quick questions about this lesson. It takes a minute, and it is how the lesson gets better.