Power functions and growth patterns

Explore power functions with integer, negative and rational exponents. This practice set connects the form of a power rule to its real domain, symmetry, graph and response to changes in input. It distinguishes a fixed exponent from an exponential rule and checks when a negative input or zero is actually allowed.

Comparing growth requires a stated input range. You will compare powers below and above one, account for coefficients, interpret a graph of two fractional-power functions and calculate multiplicative effects such as a percentage change in a squared quantity. Other questions recover a model from scaling information or examine why decreasing behavior on separate intervals does not automatically imply decreasing behavior across a disconnected domain.

Prerequisites include exponent rules, radicals, elementary function graphs and basic proportional reasoning. Rational powers use the real-root interpretation where it exists; positive inputs are used for growth comparisons unless a wider domain is explicitly discussed. Both single-select and multiselect questions progress from recognizing structure to justifying restrictions and comparisons. Explanations include useful test values and counterexamples, so you can check a claim before applying a familiar rule too broadly. No logarithms, derivatives or complex powers are required.