Comparing Linear Functions

The SAT loves to give you two functions in different forms and ask you to compare them: - Function f: given as an equation - Function g: given as a table or graph To compare, you need to extract the same information (slope, y-intercept, specific values) from each. Common comparison questions: - "Which function has the greater rate of change?" - "Which function has the greater y-intercept?" - "…

| Form | How to find slope | How to find y-intercept | |---|---|---| | Equation y = mx + b | Read m directly | Read b directly | | Table | frac{Delta y}{Delta x} from any two rows | Find or calculate f(0) | | Graph | Rise over run between two points | Read where line crosses y-axis | | Verbal | Look for "per" or "each" | Look for "starts at" or "initially" |

Example: Function f(x) = 4x + 3. Function g is given by the table: | x | g(x) | |---|---| | 0 | 10 | | 2 | 16 | | 4 | 22 | Which function has the greater rate of change? Which has the greater initial value?