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