# Function Transformations

Function:

$$f(x) = x^2$$
$$f($$$$x$$$$)$$

Value of A: 1

Value of B: 1

Value of C: 0

Value of D: 0

Starting with the graph of a function $$f(x)$$, the graph of $A f(Bx - C) + D$ is obtained by stretching the graph of $$f$$ vertically by a factor of $$A$$ and horizontally by a factor of $$B$$, while translating it vertically by a factor of $$D$$ and horizontally by a factor of $$C$$.
This applet allows you to adjust the parameters of the function $$A f(Bx - C) + D$$, where $$f(x)$$ is a quadratic, cubic, linear, or floor function. Choose a function type to transform from the drop down menu. Then, use the sliders to adjust the values of $$A$$, $$B$$, $$C$$, and $$D$$ to see how the graph changes. The transformed graph will be displayed in black. The blue dots show the original function.