Understand how shifts, reflections, stretches and compressions change the graph of a function.
Starting from y = f(x), here's how each transformation changes the graph: | Transformation | Equation | Effect | |---|---|---| | Shift up k | f(x) + k | Every point moves up k units | | Shift down k | f(x) - k | Every point moves down k units | | Shift right h | f(x - h) | Every point moves right h units | | Shift left h | f(x + h) | Every point moves left h units | | Reflect over x-axis | -f(x)…
Most SAT questions combine 2-3 transformations: g(x) = a cdot f(x - h) + k - a: vertical stretch/compression and possible reflection - h: horizontal shift (right if positive) - k: vertical shift (up if positive) Order matters: apply horizontal shift first, then stretch, then vertical shift.
Example: If f(x) = x^2, describe the transformation to get g(x) = 2(x - 3)^2 + 1.
Try NovaMaths free — AI tutoring, 95 lessons, 749+ exercises.
Practice this topic →