Comparing Linear, Quadratic, and Exponential Functions

| Property | Linear | Quadratic | Exponential | |---|---|---|---| | Equation | f(x) = mx + b | f(x) = ax^2 + bx + c | f(x) = a cdot b^x | | Graph | Straight line | Parabola | J-curve | | Growth | Constant rate (add) | Accelerating (add increasing amounts) | Multiplicative (multiply) | | Table test | Constant 1st differences | Constant 2nd differences | Constant ratios | | Key feature | Slope | Ve…

Given equally spaced x-values: 1st differences = differences between consecutive y-values. 2nd differences = differences between consecutive 1st differences. Ratios = each y-value divided by the previous one. | Pattern | Function type | |---|---| | Constant 1st differences | Linear | | Constant 2nd differences | Quadratic | | Constant ratios | Exponential |

Example: Identify the type: | x | y | |---|---| | 0 | 3 | | 1 | 7 | | 2 | 11 | | 3 | 15 |