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