1. Transformations to Parent Functions

2. Translation (Shift)
A vertical translation is made on a function by adding or subtracting a number to the function.
Example: y = x + 3 (translation up)
Example: y = x² - 5 (translation down)
A translation up is also called a vertical shift up.
A translation down is also called a vertical shift down.

3. Example: y = |x| + 2
Parent function (y = |x|) shown on graph in red.
The transformation of the parent function is shown in blue. It is a shift up (or vertical translation up) of 2 units.)

4. Example: y = x - 1
Parent function (y = x) shown on graph in red.
The transformation of the parent function is shown in blue. It is a shift down (or vertical translation down) of 1 unit.

5. Reflection
A reflection on the x-axis is made on a function by multiplying the parent function by a negative.
Multiplying by a negative “flips” the graph of the function over the x-axis.
Example: y = -x² is a reflection of the parent function y = x².

6. Example: y = - x²
The reflection of the parent function is shown in blue. It is a reflection over the x-axis of the function y = x²

7. Stretch
A stretch is made on a parent function by multiplying the parent function by a number x such that
|x| > 1.
Example: y = 3x²
A stretch is also referred to as a narrowing of the graph of the function closer to the y-axis.

8. Example: y = 2x
The blue line shows the graph of the stretch of the parent function,
y = 2x, by a scale factor of 2.

9. Shrink
A shrink is made on a function by multiplying the parent function by a number x such that 0 < |x| < 1.
Example: y = (½) x.
A shrink is also referred to as a widening of the graph of the function closer to the x-axis.

10. Example: y = (¼) x
The blue line shows the graph of the shrink of the parent function, y = (¼)x, by a scale factor of ¼.

11. What happens when we combine the two (blue is parent function)?