Domain and Range of Linear Functions

Domain = all possible input values (x-values) Range = all possible output values (y-values) Think of it this way: - Domain: "What can I put in?" - Range: "What can come out?" For a pure linear function f(x) = mx + b with no restrictions: - Domain = all real numbers (-infty < x < infty) - Range = all real numbers (-infty < y < infty) But in real-world contexts, there are usually restrictions!

Real-world problems often restrict the domain: | Context | Domain restriction | Why | |---|---|---| | Time | t geq 0 | Time can't be negative | | Quantity/count | n geq 0, integers | Can't have -3 items | | Distance | d geq 0 | Distance isn't negative | | Percentage | 0 leq p leq 100 | Bounded | The range then depends on the domain restriction combined with the function rule.

Example: A taxi ride costs C = 3.50 + 2m dollars, where m is miles. What are the domain and range?