M5.2.1 For the adult
Exponential functions
Can a number such as 2ˣ ever be zero or negative, and what does its graph look like between the whole numbers?
What this chapter teaches
In f(x) = aˣ the letter x is the power. The base a is above 0 and not 1. The graph always passes through (0, 1), stays above the x axis, and rises when a is above 1 and falls when a is between 0 and 1. The x axis is an asymptote.
Three questions to ask
There is no one right wording. Listen for the idea.
- Why does every graph y = aˣ pass through (0, 1), whatever the base?
- What changes in y = 2ˣ − 4, and what is its asymptote?
- How would you explain, in your own words, why 2ˣ can never be zero or negative?
After the chapter, the learner can
- Sketch y = 3ˣ and y = (1/2)ˣ on one grid
- Explain why aˣ is always positive
What they copy into their notebook
y = aˣ, a > 0, a ≠ 1: passes through (0, 1), always above the x axis. a > 1 grows, 0 < a < 1 decays. The x axis is an asymptote.