Identify the effect on the graph of replacing f(x) by f(Bx)

Question

1. Explanation of the transformation type and how it is identified in the equation (related to A, B, H or K)
2. Equation of an absolute value function that represents the transformation.   Explain how your example has been transformed from the parent function
3. Equation of a quadratic function that represents the transformation.  Explain how your example has been transformed from the parent function

Answer 1

Assuming B is a constant, it will compress the graph of f(x) horizontally along the x-axis by a factor of B. If B<0, it will also flip the graph across the y-axis.

In general the transformations of f(x) into g(x) are:

g(x) = A·f(B(x-C)) + D

1. A = Vertical (up/down) dilation (stretch) by a factor of A. If A < 0, it also flips the graph across the x-axis
2. B = Horizontal (left/right) compression by a factor of B. If B<0, it also flips the graph across the y-axis.
3. C = Horizontal (left/right) shift by C units. Shift right if C > 0, left if C < 0
4. D = Vertical (up/down) shift) by D units. Up if D > 0, down if D < 0.