Section 1-3 Shifting, Reflecting, and Stretching Graphs

Sunday, September 26, 2010

 

By: James Thomas


To understand how graphs can shift and reflect you must first know about the parent functions of the graph.

Parent Function: The most basic form of a equation for a graph.

Vertical and Horizontal Shifts

1) Vertical shift c units upward                    h(x)=f(x)+c
2) Vertical shift c units downward               h(x)=f(x)-c
3) Horizontal shift c units to the right          h(x)=f(x+c)
4) Horizontal shift c units to the right          h(x)=f(x-c)

Example:

              - g(x)=(x-2)²+3

Parent function = g(x)=x²
Horizontal Shift = -2....... Right Three (Translate the opposite of the sign)
Vertical Shift = +3...... Up Three





Reflecting Graphs

Graphs can also be reflected over the x-axis and y-axis depending on a (-) sign in the equation.

- Reflection over the x-axis                    h(x)=-f(x)
- Reflection over the y-axis                    h(x)=f(-x)

Example:



Nonrigid Transformations:

- Rigid Transformations- Horizontal and Vertical Shifts because they dont affect the graphs shape or structure, just the location.
- Nonrigid Transformations - Causes a distortion in the graph making it skinnier or fatter.

                      y=cf(x)
- Skinny Transformation = 0 < c < 1
- Fatter Transformation = c > 1


Example:

            - g(x) = 3x^{2 ,}           g(x)= 1/4x²