Transformations of Graphs

Basic laws

• $f(x)+c$ … move along by $c$ units along y axis
• $f(x+c)$ … move along by $c$ units along x axis (inversed)
• $c\ast f(x)$ … stretch ($c>1$) (or compress $1>c>0$) vertically or flip it along x-axis ($c<0$)
  • this can also shift along y-axis
  • $f(x)=sin(x)+3)$ has its center value at 2 ($2<f(x)<4$)
  • $g(x)=2\ast f(x)$ has its center value at 6 ($4<f(x)<8$)
• $f(c\ast x)$ … compress ($c>1$) (or stretch $1>c>0$) vertically or flip it along y-axis ($c<0$)