Every graph in this course is some parent function that has been moved, resized, or flipped. Master one formula — g(x) = af(x − h) + k — and you can graph all of them without plotting a single table of values. Drag the three knobs and watch what each one actually does.
The graph
parent current graph moved points the one we check
Where every point lands
1 · Pick a parent function
2 · Drag the three knobs
a stretch / reflect1
−303
h horizontal shift (inside)0
−606
k vertical shift (outside)0
−606
Horizontal—
Vertical size—
Vertical shift—
3 · Build it up, one change at a time
The one rule to remember: changes outside the function (a and k) affect the outputs — heights — and do exactly what they say. Changes inside the function (h) affect the inputs and do the opposite of what they look like.