[size=150]The [b]Parent [color=#e06666]Cube Root[/color] Function[/b] is [math]f\left(x\right)=\sqrt[3]{x}[/math]. The [b]"kid"[color=#e06666] CubeRoot [/color]function is[/b] given by the equation, [math]f\left(x\right)=a\sqrt[3]{bx-h}+k[/math]. With this activity, you will explore the values of [i]a, h, [/i]and [i]k[/i], and what effect these values have on the kid function![/size][br][br][size=150][b][color=#e06666]YOU TRY: Set your [i]a [/i]slide bar to "1" and the other slide bars to "0." [/color][/b]What you see is the PARENT [color=#e06666][b]Cube Root[/b] [/color]FUNCTION. Draw a sketch of this graph. Record the vertex, x-intercept, Domain & Range.[br][br][i]*[/i]NOTE: [i]The cube root function is the inverse of a cubic function, so it's a sideways-S, rather than an upright-S.[/i][br][br][b][color=#e06666]YOU TRY: Use the slide bars to change the values of [/color][/b][b][color=#e06666][i]a, h, [/i]and [/color][i][color=#e06666]k. Change them in multiple ways![br][br][/color][/i][/b][/size][size=150]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.[/size][br][br][size=150][color=#e06666][i]1. What does the "a" do to the graph? Be specific. HINT! It can do THREE things.[br][/i]2. [i]What does the "h" do? Be specific.[br]3.[/i] [/color][i][color=#e06666]What does the "k" do? Be specific.[br][/color][/i][/size][br][size=150]The [b]domain[/b] and [b]range[/b] of the Parent Square Root Function is [math]\mathbb{R}[/math]or([math]\infty,\infty[/math]).[/size][br][br][b][size=150][color=#e06666]YOU TRY: How does manipulating the values of [i]a, h[/i] and [i]k[/i] affect the domain and range? [/color][/size][/b]