Students can change the functions to practice transforming parent functions using translations, reflections, stretching, and shrinking.

Use the following transformations to write an equation for the new image g(x). Then check your equation by changing g(x) on the left side. Sketch the new image.
a. Translation 4 units to the right and 2 units down
Equation:
Sketch f(x) and g(x) after the transformation.
b. Reflection over the x-axis and translation 3 units to the left.
Equation:
Sketch f(x) and g(x) after the transformation.
2) What operations on f(x) would produce the following transformation to g(x)?
g(x) =
3) What operations on f(x) would produce the following transformation to g(x)?
g(x) =
4) For questions 1-3, what is the parent function?
5) Now change f(x) = x2 to f(x) = abs(x).
a. What graph does this create?
b. What equation would you need to put in for g(x) to get a reflection over the x-axis?
c. Sketch f(x) and g(x) below.
6) Now let both f(x) and g(x) = -abs(x).
What operations on f(x) would produce the following image?
7) What is the parent function for questions 5-6?
8) How did this activity using GeoGebra help you review?
9) Would you prefer using GeoGebra or a calculator to see the transformations? Why?