GeoGebra Exploration: The Cube Root Function
The Parent Cube Root Function is . The "kid" CubeRoot function is given by the equation, . With this activity, you will explore the values of a, h, and k, and what effect these values have on the kid function!
YOU TRY: Set your a slide bar to "1" and the other slide bars to "0." What you see is the PARENT Cube Root FUNCTION. Draw a sketch of this graph. Record the vertex, x-intercept, Domain & Range.
*NOTE: The cube root function is the inverse of a cubic function, so it's a sideways-S, rather than an upright-S.
YOU TRY: Use the slide bars to change the values of a, h, and k. Change them in multiple ways!
What do you notice? Record your observations onto a sheet of paper or create a Google doc with your notes. Pay particular attention to the questions below.
1. What does the "a" do to the graph? Be specific. HINT! It can do THREE things.
2. What does the "h" do? Be specific.
3. What does the "k" do? Be specific.
The domain and range of the Parent Square Root Function is or().
YOU TRY: How does manipulating the values of a, h and k affect the domain and range?