You have probably graphed functions such as y=x, y=x^2, y=|x|,
etc....
In fact, you might already know what each of these
functions looks like by memory.
For instance:
- y=x is a diagonal line through the origin
- y=x^2 is a parabola with its vertex on the origin
- y=|x| is a V with its vertex on the origin
These graphs are called parent functions
Now we are going to explore graphs that look very similar
to those that we already know. These graphs have been transformed from their parent functions. We can transform
a function in three ways:
- translation - This transformation
slides the graph around. A vertical translation moves the graph up or down, while a horizontal translation
moves the graph left or right.
- stretch or shrink - This transformation
is just as it sounds. It vertically stretches or shrinks the graph.
- reflection - This transformation flips the
graph over the x or y axis.
Go to the "How Do We Transform a Function?" page to learn how each of these transformations
work.
