# Function Transformations

[left][color=#000000]This applet accompanies the [/color][i][color=#1e84cc][b]Transformations of Functions[/b][/color][/i][color=#000000] packet you received at the beginning of class. [/color][/left]

# Transformations of Graphs (a, h, k)

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

Questions: [br][br]1) 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? [br]2) 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? [br]3) 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?