Interpreting parameters and asymptotic behavior

Teacher tools for this standard

Lesson Plan · Guided Notes · Exit Ticket · Re-teach · Homework

Lesson Plan →Objectives, pacing and practice, built from this lesson's brief.
Guided Notes →One page your students fill in and keep.
Exit Ticket →Three items at the end of class. No student accounts.
Re-teach →After an exit ticket: who missed what, and what to do tomorrow.
Homework →Assign practice; it grades itself.

**AF 705.** Identify characteristics of graphs based on a set of conditions or on a general equation such as y = ax² + c — score range 33-36, lines 371-372 **F 510.** Find where a rational function's graph has a vertical asymptote — score range 24-27, lines 288-290 **F 702.** Build functions for relations that are exponential — score range 33-36, lines 391-392

AF 705. Identify characteristics of graphs based on a set of conditions or on a general equation such as y = ax² + c — score range 33-36, lines 371-372
F 510. Find where a rational function's graph has a vertical asymptote — score range 24-27, lines 288-290
F 702. Build functions for relations that are exponential — score range 33-36, lines 391-392

What you'll learn

Identify $a$, $b$, and $k$ in $y = ab^x + k$ and state what each controls on the graph
Predict the horizontal asymptote of $y = ab^x + k$ as $y = k$, and explain why the graph approaches but never reaches it
Describe the end behavior of an exponential function in both directions from the value of $b$
Compare two exponential functions given as equations, and say which starts higher and which eventually wins
Read $a$, $b$, and $k$ off a graph or table and reconstruct the equation, working asymptote first
Distinguish the effect of changing $a$ (vertical scaling) from changing $k$ (vertical shift)

Review first:

Exponential growth and decay

Slides

Step through the lesson, or watch it as a narrated video

Slides

In development

Not yet available • Check back soon!

Was this lesson helpful?

Report a problem with this page