Transformation of Curves Questions with Solutions

Transformation of curves is about how the graph of a function changes when its equation is modified. If you know the graph of y = f(x), you can sketch related graphs without plotting points. This topic covers shifts (y = f(x) + k moves the graph up, y = f(x - h) moves it right), reflections in the axes (y = -f(x) and y = f(-x)), stretches and compressions (y = af(x) and y = f(ax)), and graphs involving modulus such as y = |f(x)| and y = f(|x|). Exam questions ask you to identify the graph of a transformed function, find the new position of a point or vertex, or count the solutions of an equation using graphs. A common trap is the direction of horizontal shifts: f(x - 2) moves the graph two units to the right, not the left. Practise the transformation of curves questions below, each with a step-by-step solution.