Identify transformations of graphs

Start lessonBegins with Identify graph transformations shifts · Slides

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.

HSF.BF.B.3

**HSF.BF.B.3**: Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

HSF.BF.B.3: Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

What you'll learn

Identify and graph vertical translations: f(x) + k shifts the graph up (k > 0) or down (k < 0) by |k| units
Identify and graph horizontal translations: f(x + k) shifts the graph left (k > 0) or right (k < 0) by |k| units
Identify and graph vertical stretches/compressions and reflections: kf(x) stretches vertically by |k|, reflects over x-axis when k < 0
Identify and graph horizontal stretches/compressions and reflections: f(kx) compresses horizontally by |k|, reflects over y-axis when k < 0
Determine the value of k given the graphs of f(x) and a transformed version
Recognize even functions (f(-x) = f(x), symmetric about y-axis) and odd functions (f(-x) = -f(x), symmetric about origin) from graphs and algebraic expressions

Review first: