Here are the required notes for your convenience.
Two graphs may look exactly alike in shape, but differ in their positions within the xy-plane.
Adding or subtracting values from a function will shift the graph of the function on the coordinate plane.
If f is a function and c is a positive constant, then the graph of
- is the graph of shifted up c units
- is the graph of shifted down c units
- is the graph of shifted left c units
- is the graph of shifted right c units
Vertical translations: adding or subtracting after the function (outside the parenthesis)
shifts up 3 spaces on the y axis
shifts down 2 spaces on the y axis
Horizontal translations: adding or subtracting with the function (inside the parenthesis)
shifts the graph of left 4 spaces on the x axis
shifts the graph of right 3 spaces on the x axis
Vertical & Horizontal translation
shifts the graph of up 2 spaces on the y-axis and right 5 on the x-axis.
If , , and
Find the coordinates for h(x) = f(x) + 5 and g(x) = f(x – 2)