Consider the function [b]y = f(x)[/b]. We're going to refer to this function as the [b]PARENT FUNCTION[/b]. [b]The following applet allows you to select one of 4 parent functions: [/b] The basic quadratic function: f(x) = x^2 The basic cubic function: f(x) = x^3 The basic absolute value function: f(x) = |x| The basic square root function: y = sqrt(x) [b]In each of these functions, you will investigate what the parameters "a", "h", & "k" will do to the graph the parent function y = f(x) when we graph the function y = a*f(x - h) + k[/b] The following applet allows you to use a slider to change the values of different [b]parameters[/b] of 4 [b]key functions[/b]. The parameters are "[color=#c51414]a[/color]", "[color=#0a971e]h[/color]", and "[color=#1551b5]k[/color]". Within the following applet, change the slider values for "[color=#c51414]a[/color]", "[color=#0a971e]h[/color]", and "[color=#1551b5]k[/color]". As you do, pay attention to how the equation of the graph changes as you use the slider to change a certain parameter. [b]Be sure to pay close attention as you change parameters, one at a time, for EACH of the four functions listed below. [/b] After interacting with this applet for a few minutes, answer the questions (below the applet) as specifically as you can.

Questions: [list] H1) For any value "[color=#0a971e]h[/color]", how does the parameter "[color=#0a971e]h[/color]" affect the graph of a function? If [color=#0a971e]h[/color] > 0, what happens? If [color=#0a971e]h[/color] < 0, what happens? H2) How would we have to move the curve [color=#b20ea8]y = f(x)[/color] to get the curve [color=#b20ea8]y = f(x + 12)[/color]? K1) For any value "[color=#1551b5]k[/color]", how does the parameter "[color=#1551b5]k[/color]" affect the graph of a function? If [color=#1551b5]k[/color] > 0, what happens? If [color=#1551b5]k[/color] < 0, what happens? K2) How would we have to move the curve [color=#b20ea8]y = f(x)[/color] to get the curve [color=#b20ea8]y = f(x) + 12[/color]? A1) For any value "[color=#c51414]a[/color]", how does the parameter "[color=#c51414]a[/color]" affect the graph of a function? If [color=#c51414]a[/color] > 0, what happens? If [color=#c51414]a[/color] < 0, what happens? A2) How would we have to move the curve [color=#b20ea8]y = f(x)[/color] to get the curve [color=#b20ea8]y = - f(x)[/color]? A3)How would we change the curve [color=#b20ea8]y = f(x)[/color] to get the curve [color=#b20ea8]y = 3 f(x)[/color]? Final Question: How would we change the curve [color=#b20ea8]y = f(x)[/color] to get the curve [color=#b20ea8]y = - f(x+3) - 8[/color]? (Play with the sliders to determine the appropriate order to transform your graph in!) [/list]