Math141 Chapter 1.6 Transformations of Functions

Math 141 (Precalculus I) – Section 1.6: Transformations of Functions In this lesson we learn how to shift, stretch, shrink, and reflect a graph by changing its equation. We start with the transformation rules, then practice them on worked examples. You'll see why changes inside f(x) do the opposite of what you expect, while changes outside do exactly what they say. What's covered: • Vertical and horizontal shifts • Reflections about the x-axis and y-axis • Vertical and horizontal stretches and shrinks • The order for applying transformations: horizontal shift → stretch/shrink/reflect → vertical shift • Graphing by tracking points (new x, new y) • Finding the domain and range of a transformed function • Identifying parent functions: √x, |x|, x² • Application: shifting a thermostat schedule • Writing an equation from a graph Chapters: 0:00 Intro 0:02 Transformation rules & rules of thumb 2:15 Describing transformations from an equation 4:03 Graphing by tracking points: g(x) = 2f(x − 3) − 1 6:27 Graphing h(x) = −f(½x) + 2 7:37 Parent functions: g(x) = √(−x + 3) 10:13 f(x) = −½|x − 1| + 4 12:50 h(x) = 2∛(x + 1) − 3 13:31 Application: thermostat schedule 15:36 Writing equations from graphs (square root) 16:53 Writing equations from graphs (parabola) Tip: pause the video and try each problem on your own before watching the solution. 👍 If this helped, like and subscribe to Carmen Does Math for more videos. #Precalculus #TransformationsOfFunctions #MathHelp #CarmenDoesMath