Lesson Plan

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

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