Evaluating Functions over Equal Intervals
These materials, when encountered before Algebra 1, Unit 5, Lesson 20 support success in that lesson.
In the associated Algebra 1 lesson, students rewrite expressions with the goal of showing that for any equal intervals of the independent variable, an exponential function always changes by an equal factor and a linear function always changes by an equal difference. In this lesson, students practice using the properties they will need to rewrite expressions, including exponent properties and applying the distributive property with a negative coefficient. When students repeatedly perform calculations and then generalize, they are expressing regularity in repeated reasoning (MP8). If students decide to use technology to efficiently evaluate the same function for different input values, they are using appropriate tools strategically (MP5).
- Rewrite expressions of the types needed to show that linear functions change by equal differences over equal intervals and exponential functions change by equal factors over equal intervals.
- Let’s evaluate and rewrite expressions.