Shifting Functions Math

The graphs of many functions are transformations of the graphs of very basic functions.

Shifting functions math. So everything that is left of the origin is shifted further to the left and everything on the right is shifted further to the right. A point a b a b on the graph of y f x y f x moves to a point a b p a b p on the graph of y f x p y f x p. This is a vertical shift. A vertical shift adds subtracts a constant to from every y coordinate while leaving the x coordinate unchanged.

The graph of y x2 3 is the graph of y x2 shifted upward three units. Shift functions horizontally and vertically and practice the relationship between the graphical and the algebraic representations of those shifts. Subtracting p p from the previous y y values gives the new equation y f x p y f x p. Similarly the graph of y f x h where h is a real number is the same as the graph of y f x only it s shifted to the right when h 0 or to the left when h 0.

Start with the equation y f x y f x. If we scale it along the y axis by a factor of 10 then where the function value was 10 before it would now be 100. All that a shift will do is change the location of the graph. If you re seeing this message it means we re having trouble loading external resources on our website.

Y f x 3 2 again students wonder why the upward shift of 2 is done with 2 while the shift to the right is done with 3. The usual approach uses the notation. This shifts the graph down p p units. X y 4 4 4 4 8 8 y x2 y x2 3 y x2.

A horizontal shift adds subtracts a constant to from every x coordinate while leaving the y coordinate unchanged. Scaling means shrinking or magnifying the function. The graph of y f x k where k is a real number is the same as the graph of y f x only it s shifted up when k 0 or down when k 0. Y f x h k to move the graph 3 units right and 2 units up we would have.

The graph of y x2 is the reflection of the graph of y x2 in the x axis.