A change outside the f acts on y and does what it looks like: f(x) + 2 moves the graph 2 units in the positive y-direction, and 3f(x) is a scaling parallel to the y-axis with factor 3.
A change inside the bracket acts on x and does the opposite of what it looks like: f(x + 2) moves the graph 2 units in the negativex-direction, and f(3x) is a scaling parallel to the x-axis with factor 1/3.
A scaling or reflection leaves the points on its own axis where they are: y = af(x) keeps the x-intercepts, and y = f(ax) keeps the y-intercept.
Asymptotes move with the graph. A vertical asymptote is only affected by changes to x, a horizontal one only by changes to y.
What to notice
Two steps that act on different variables — one on x, one on y — can be done in either order.
Two steps on the same variable often cannot. To get y = f(2x + 3), translate 3 units in the negative x-direction and then scale with factor 1/2 — or scale first, and then translate by only 3/2 units.
To describe a sequence for a given equation, build the equation up from y = f(x) one replacement at a time, and state each step in the order you made it.
This is how we teach H2 Maths
Tools like this one are part of our H2 Maths lessons. Sit in on a lesson for free, then decide.
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