Kick off your Pre-Calculus unit with a lesson that truly brings functions to life! This comprehensive 196-slide resource dives deep into every major transformation—horizontal and vertical translations, reflections, stretches, compressions, and even combining transformations with precision and clarity. Students will build confidence as they explore each concept through step-by-step explanations, fully worked examples, interactive demonstrations, and tons of practice problems (with answers included!). Plus, the lesson wraps up with a clear introduction to the inverse of a relation, helping learners make essential Pre-Calculus connections. Perfect for engaging whole-class instruction, guided practice, or independent learning—this is Lesson 1 done right!

Lesson Objectives

1-1 Horizontal and Vertical Translations

• Determining the effects of h and k in y - k = f(x - h) on the graph of y = f(x).
• Sketching the graph of y - k = f(x - h) for given values of h and k, given the graph of y = f(x).
• Writing the equation of a function whose graph is a vertical and/or horizontal translation of the graph of y = f(x).

1-2 Reflections and Stretches

• Developing an understanding of the effects of reflections on the graphs of functions and their related equations.
• Developing an understanding of the effects of vertical and horizontal stretches on the graphs of functions and their related equations.

1-3 Combining Transformations

• Sketching the graph of a transformed function by applying translations, reflections, and stretches.
• Writing the equation of a function that has been transformed from the function y = f(x).

1-4 Inverse of a Relation

• Sketching the graph of the inverse of a relation.
• Determining if a relation and its inverse are functions.
• Determining the equation of an inverse.