Graphs of functions

Graphs of functions. If we know the graph of $f$, we can sketch the graphs of $ f(x) = x^2 + 4$, $ f(x) = (x - 4)^2$, etc.

Equation of Effect on the graph of $f$
$ {y = f(x) + c}$ Shift it vertically upward if $ c > 0$, or downward if $ c < 0$.
$ {y = f(x + c)}$ Shift it horizontally to the left if $ c > 0$, or to the right if $ c < 0$.
$ {y = c f(x)}$ Stretch it vertically if $ 1 < c$, or compress it vertically if $ 0 < c < 1$.
$ {y = f(c x)}$ Stretch it horizontally if $ 1 < c$, or compress it horizontally if $ 0 < c < 1$.



Department of Mathematics
Last modified: 2005-09-29