Work with linear, quadratic, polynomial, exponential, logarithmic, radical, and piecewise functions.
Match a function family to its pattern of change and graph shape.
核心知识
Each function family has a recognizable pattern. Linear functions change by equal differences, quadratics bend once, exponentials change by equal ratios, radicals begin at an endpoint, logarithms grow slowly after a restriction, and piecewise functions switch rules across intervals.
深入理解
Rule: On ACT, you do not need a long theory lecture for each function family. You need quick recognition. Ask what stays consistent: equal differences suggest linear behavior, equal multiplicative change suggests exponential behavior, and a defined starting point with a square-root shape suggests a radical function.
That recognition helps you choose the right model and avoid forcing the wrong form onto the situation. A quantity that grows by a fixed percent is not linear. A rule that changes at a cutoff point probably needs a piecewise definition. A curve with one turning point may be quadratic rather than exponential.
分步讲解
- Look for the pattern in how outputs change as inputs increase.
- Match the pattern to the function family before writing an equation.
- Check whether the context describes additive change, multiplicative change, or a rule that switches by interval.
- Use domain clues to help distinguish radical, logarithmic, and piecewise models.
示例解析
A bacteria culture starts with 200 cells and increases by 12% each hour. Which function could model the number of cells after
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