Graphing Exponential Functions
I can graph an exponential function and name its intercept and asymptote.
The problem this sheet solves
At x = −6, 2 to the x is about 0.0156, which rounds to 0.02 on a table and IS the axis on a printed grid. So a student who says the curve crosses is reading their evidence correctly. Telling them to look closer does not work, because looking closer is what produced the error. This sheet argues from the EQUATION rather than the picture: 2 to the x equals 0 has no solution, and that settles what no amount of zooming can. The asymptote is drawn as a dashed line the curve never meets, and shifted graphs are included so students learn the asymptote is not always the x-axis.
The key rule
An exponential curve APPROACHES its asymptote and never touches it. bx is positive for every x, so y = bx has no x-intercept.
Closer forever. Never zero.
Watch out
The mistake: A student graphs y = 2x and says it crosses the x-axis at x = −6.
The fix: At x = −6 the value is 1/64, about 0.0156 — small, but positive. And 2x = 0 has no solution, so there is no crossing.
What is included
- Reference page — student-friendly definitions, a worked example, a Watch Out error pair, and the key rule
- Practice page — six problems, building from foundational to multi-step
- Apply page — a word problem, a reasoning prompt, and an error-analysis task
- Assess — a half-page exit ticket, two to a sheet, with a score box
- Full answer key — every item worked, plus a grading guide that says what each wrong answer tells you
- Ink-saver edition of all 7 pages
- 14-slide teacher deck (PowerPoint) with presenter notes on every slide
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.