Vertical and Horizontal Linear Transformations
The Original Function f(x)
Begin by adjusting the sliders in green to change the values of m and b. The line in green, f(x), is our original function. Adjust each slider one at a time, and test out all kinds of different values for each slider. Then respond to the questions below based on your observations.
What happens when you adjust the slider labeled 'm'? What does 'm' represent about the line in green?
What happens when you adjust the slider labeled 'b'? What does 'b' represent about the line in green?
The Transformed Function g(x)
The blue function g(x) represents a transformation of the original function f(x) by a constant to the function f(x). Adjust the blue slider labeled 'k'. After exploring all kinds of different values, respond to the questions below based on your observations.
What happens when you adjust the slider labeled 'k'? What does this change about the graph of our original function f(x)?
The Transformed Function h(x)
The red function h(x) represents a transformation of the original function f(x) by adding a constant amount directly to the input. Adjust the red slider labeled 'h'. After exploring all kinds of different values, respond to the questions below based on your observations.
What happens when you adjust the slider labeled 'h'? What does this change about the graph of our original function f(x)?