TRANSFORMATION OF FUNCTIONS
A change in the position, shape, or size of a graph is called a transformation. The types of transformations we focus on is either a vertical or horizontal translation or a reflection across the x-axis.
In order to understand these transformations, we need to know the general shape of the basic function of each category called the parent function. Examples are shown below including their function.
When doing transformations, we use the following for each section to represent those changes.
Linear
Exponential
Cubic
Absolute Value
Exponential
If you notice, all of these have the same three parts in common; a, h, and k.
The a tells us one of two things. If it is positive, it's the same general shape as the parent. If it is negative however, it will reflect across the x-axis. If writing a function and it does not reflect, you don't have to put any value for a.
The h value tells us the horizontal shift. If h is positive, the graph shifts to the left. If h is negative, the graph shifts to the right. A tip I use to remember this is if it is inside "parentheses", move opposite.
The k value tells us the vertical shift. If k is positive, the graph shifts up. If k is negative, the graph shifts down.
