Graphing Exponential Functions
I can graph an exponential function from a table and give its y-intercept, asymptote, domain and range.
What students learn
Students learn to make a table for y = a · bˣ, graph it, and explain why the curve gets closer and closer to the x-axis but never touches it.
See inside
The key rule
Each step left divides by b. That never reaches 0, so bˣ is positive for every x.
y = a · bˣ: (0, a); asymptote y = 0
Every function y = a · bˣ on this sheet has a > 0: domain all real numbers, range y > 0, no x-intercept.
Watch out
A student graphs y = 3ˣ and says it meets the x-axis at x = −4.
The mistake: 3⁻⁴ is 0, so (−4, 0)3⁻⁴ is small, but it is not 0.
The fix: 3⁻⁴ = 1/81 > 0: it never meets the axisA positive base to any power is positive.
The mistakes it targets
- Calls a small positive value 0, so the curve meets the x-axis
- Uses the base as the y-intercept
- Puts 0 in the range of an exponential function
- Reads a negative exponent as a negative number
- Keeps y = 0 as the asymptote after the graph is shifted up
The interactive Teacher Deck (32 slides, PowerPoint)
- The Learn page taught on screen: 8 fill-in blanks, each filled on its own click as students write it
- The worked example one slide per step (four steps), each with the reason for the step
- Six practice and three apply problems: a your-turn slide with a think-time bar, then the solution one line per click
- Jump buttons on every slide: go straight to any problem, the answer bank or the exit ticket
- Speaker notes on each problem: the question to ask, the worked answer and the common error to listen for
- A completed deck PDF (19 pages) with every slide fully built, to print or post
The student packet (9 pages)
- Learn: guided notes with four definitions, the key rule, a worked example and a Watch Out error pair
- Practice: two warm-up, two standard and two stretch problems, with an answer bank for self-checking that hides three common-mistake decoys
- Apply: one word problem, a reasoning prompt and one error analysis
- Assess: an exit ticket of four items, two per page, with an I-can self-rating
- Homework (page 5): eight new problems, two warm-up, four standard and two stretch
- Answer key (pages 6–7): every problem worked step by step, five common mistakes with what to do about each, and a grading guide, plus the homework key (page 8)
- Color and ink-saver editions of the whole packet
Standard codes refer to the Common Core State Standards for Mathematics. Math Class 678 is an independent publisher, not affiliated with, sponsored by, or endorsed by NGA Center or CCSSO. Every product is sold on Teachers Pay Teachers.