Power functions may look scary at first, but they follow clear patterns once you know what to observe. In Secondary 3 and 4 Mathematics, recognising the shape, symmetry, and direction of a graph can help you sketch faster and avoid careless mistakes.

For example, y=x2y=x^2 forms a U-shape, while y=−x2y=-x^2 is reflected downwards. Cubic graphs like y=x3y=x^3 and y=−x3y=-x^3 curve in opposite directions. Reciprocal graphs such as y=axy=\frac{a}{x} and y=ax2y=\frac{a}{x^2} have separate branches and do not touch the axes.

Instead of memorising every graph blindly, ask yourself: Is the power odd or even? Is there a negative sign? Is the variable in the denominator? These small clues can tell you a lot about the graph before you even draw it.

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