Evaluate Piecewise Numerical Expressions

What this means

A piecewise expression gives different rules for different values of the input. Your job is to pick the correct rule, substitute the given number, and simplify.

Step-by-step method

1. Identify the input value. Look carefully at the number you are asked to evaluate.
2. Choose the matching piece. Find the condition that includes that input. For example, one rule may apply when the input is less than a certain number, and another when it is greater than or equal to it.
3. Substitute the value. Replace the variable in the selected expression with the given number.
4. Simplify completely. Carry out arithmetic in the correct order.

Important tip

Only one rule should apply. If the boundary value is included with symbols like ≤ or ≥, use that rule at the endpoint.

Check your work

After evaluating, plug the input back into the condition to make sure you chose the right rule. Then verify that the final number is reasonable and that the expression is simplified.