Math basics › Functions and graphs
Transformations
Outside changes y, inside changes x
f(x) + 2 moves up. f(x + 2) moves left — inside the bracket, it goes the opposite way to what you expect.
Stretches
a·f(x) stretches vertically by a. f(bx) squashes horizontally by b.
Reflections
−f(x) flips over the x-axis. f(−x) flips over the y-axis.
Order matters
Stretch before shift, or you will move the wrong distance.