# Transformations of Graphs (a, h, k)

Consider the function y = f(x). We're going to refer to this function as the PARENT FUNCTION. The following applet allows you to select one of 4 parent functions: 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) 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 The following applet allows you to use a slider to change the values of different parameters of 4 key functions. The parameters are "a", "h", and "k". Within the following applet, change the slider values for "a", "h", and "k". As you do, pay attention to how the equation of the graph changes as you use the slider to change a certain parameter. Be sure to pay close attention as you change parameters, one at a time, for EACH of the four functions listed below. After interacting with this applet for a few minutes, answer the questions (below the applet) as specifically as you can.
Questions:
H1) For any value "h", how does the parameter "h" affect the graph of a function? If h > 0, what happens? If h < 0, what happens? H2) How would we have to move the curve y = f(x) to get the curve y = f(x + 12)? K1) For any value "k", how does the parameter "k" affect the graph of a function? If k > 0, what happens? If k < 0, what happens? K2) How would we have to move the curve y = f(x) to get the curve y = f(x) + 12? A1) For any value "a", how does the parameter "a" affect the graph of a function? If a > 0, what happens? If a < 0, what happens? A2) How would we have to move the curve y = f(x) to get the curve y = - f(x)? A3)How would we change the curve y = f(x) to get the curve y = 3 f(x)? Final Question: How would we change the curve y = f(x) to get the curve y = - f(x+3) - 8? (Play with the sliders to determine the appropriate order to transform your graph in!)