Function transformations homework

Function Transformations. Let us start with a function, in this case it is f(x) = x 2, but it could be anything: f(x) = x 2. Here are some simple things we can do to move or scale it on the graph: g(x) = x 2 + C. Note: to move the line down, we use a negative value for C. C > 0 moves it up.

We can move it left or right by adding a constant to the x-value: g (x) = (x+C)2 Adding C moves the function to the left (the negative direction).

We can stretch or compress it in the y-direction by multiplying the whole function by a constant. We can stretch or compress it in the x-direction by multiplying x by a constant. We can flip it upside down by multiplying the whole function by −1: We can flip it left-right by multiplying the x-value by −1:

Summary y = f (x) + C C > 0 moves it up C 0 moves it left C 1 stretches it in the y-direction 0 ... y = f (Cx) C > 1 compresses it in the x-direction 0 ... y = −f (x) Reflects it about x-axis 1 more rows ...