Lesson Plan

Describe the effect of $a$ in $y = a f(x)$ on the graph, distinguishing $|a| > 1$ from $0 < |a| < 1$

Identify graph characteristics — opening direction, relative width, and a named point's image — from an equation of the form $y = ax^2 + c$

Describe the effect of a negative coefficient: $y = -f(x)$ reflects across the x-axis, $y = f(-x)$ across the y-axis

Apply the point-mapping rules $(p,q) \mapsto (p, aq)$ for a vertical stretch and $(p,q) \mapsto (p,-q)$ for an x-axis reflection

Write the equation of a parent function subjected to a stated stretch, compression, or reflection

Describe the effect of $b$ in $y = f(bx)$ on a graph's horizontal extent

AF 705. Identify characteristics of graphs based on a set of conditions or on a general equation such as y = ax² + c G 607. Find the coordinates of a point reflected across a vertical or horizontal line or across y = x AF 703. Analyze and draw conclusions based on properties of algebra and/or functions F 705. Match graphs of basic trigonometric functions with their equations AF 604. Given an equation or function, find an equation or function whose graph is a translation by a specified amount up or down