This worksheet is an inquiry-based activity used to explore the effects of graph transformations on various parent functions.

Part 1[br]Type x^2 into the input box and press enter. [br]Click the yellow button to explore the graph of g(x)=a*f(x). [br]Move the slider to change the value of a. [br]Make a conjecture about how the value of a transforms the graph of f(x) to the graph of g(x). [br][br][br][br][br]Repeat the same work with the following functions and test your conjecture. [br]x3 (type x^3)[br]|x| (type abs(x))[br]√x (sqrt(x))[br]Does your conjecture hold? If not change it.[br][br][br][br]Does your conjecture hold if 0<a<1? If not, modify it.[br][br]Does your conjecture still hold if a < 0? If not, modify it.[br][br]Does your conjecture still hold if a = 0? If not, modify it.[br][br][br]Part 2.[br]Type x^2 into the input box and press enter. [br]Click the green button to explore the graph of g(x)=f(x-h). [br]Move the slider to change the value of h. [br]Your task consists of making a conjecture about how the value of h transforms the parent function. [br]Observe the transformations of the graph with the changes of the value h.[br]Do the same using the following functions: x3 (type x^3) ; |x| (type abs(x)); and √x (sqrt(x))[br]Based upon your observations, make a conjecture on how the value of “h” affects the graph of the equation g(x)=f(x-h). [br][br]Does your conjecture hold for h>0? If not, modify your conjecture.[br][br]Does your conjecture hold for h<0? If not, modify your conjecture.[br][br][br][br][br]Part 3.[br]Type x^2 into the input box and press enter. [br]Click the blue button to explore the graph of g(x)=f(x)+k. [br]Move the slider to change the value of k. [br]Your task consists of making a conjecture about how the value of k transforms the parent function. [br]Observe the transformations of the graph with the changes of the value k.[br]Do the same using the following functions: x3 (type x^3) ; |x| (type abs(x)); and √x (sqrt(x))[br]Based upon your observations, make a conjecture on how the value of “h” affects the graph of the function g(x)=f(x)+k. [br][br][br][br]Does your conjecture hold for k>0? If not, modify your conjecture.[br][br][br]Does your conjecture hold for k<0? If not, modify your conjecture.[br][br][br]Part 4[br]Type x^2 into the input box and press enter. [br]Click the red button to explore the graph of g(x)=a*f(x-h)+k. [br]Move the sliders to change the values of a, h, and k. [br]Observe how each of these values transforms the five parent functions and check the conjectures you have made.

This worksheet is an inquiry-based activity used to explore the effects of graph transformations on various parent functions.