Learning Goal
Interpreting parameters and asymptotic behavior
Teacher tools for this standard
Lesson Plan · Guided Notes · Exit Ticket · Re-teach · Homework
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 604.** Given an equation or function, find an equation or function whose graph is a translation by a specified amount up or down — score range 28-32, lines 313-314
**AF 706.** Given an equation or function, find an equation or function whose graph is a translation by specified amounts in the horizontal and vertical directions — score range 33-36, lines 373-375
**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
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AF 604. Given an equation or function, find an equation or function whose graph is a translation by a specified amount up or down — score range 28-32, lines 313-314
AF 706. Given an equation or function, find an equation or function whose graph is a translation by specified amounts in the horizontal and vertical directions — score range 33-36, lines 373-375
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, distinguishing scaling by $a$ from shifting by $k$
- Predict the horizontal asymptote of $y = ab^x + k$ as $y = k$, explain why the graph approaches but never reaches it, and state the range: $b^x$ takes every positive value exactly once
- 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 and reconstruct the equation, working asymptote first
Slides
Step through the lesson, or watch it as a narrated video
Slides
In development
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