Quick questions on Sketching graphs by transformation - TCE Mathematics Specialised (Tasmania)

For a parent $y = f(x)$, the transformed graph

When more than one transformation acts, order can matter. A safe approach is to deal with horizontal changes (inside $f$) by factorising so the coefficient of $x$ is clearly separated, and to apply dilations before translations when reading the standard form. The reliable check is to track one or two key points (such as an intercept or a turning point) through each step.

To sketch $y = f(x) + g(x)$ graphically, sketch $f$ and $g$ on the same axes, then at chosen $x$ values add the two heights (ordinates). Key anchor values to use: where either function is zero (the sum equals the other function there), and where the two graphs cross.