Writing Function Rules from Word Problems
Writing function rules from word problems is a Grade 7 algebra skill in Big Ideas Math Advanced 2, Chapter 6: Functions. Students identify the independent variable (input) and dependent variable (output), then express the relationship as y equals f(x). For example, a plumber charging 50 dollars plus 75 dollars per hour gives the function C equals 75h plus 50, where h is hours worked and C is total cost.
Key Concepts
To write a function rule from a word problem, identify the independent variable (input), dependent variable (output), and the mathematical relationship between them. Express this relationship as an equation in the form $y = f(x)$ where $x$ is the independent variable and $y$ is the dependent variable.
Common Questions
How do you write a function rule from a word problem?
Identify the independent variable (what you control) and dependent variable (what changes as a result), look for key mathematical words like per or times, and write the relationship as y equals f(x).
What keywords indicate mathematical operations in word problems?
Per and each indicate multiplication or a rate. Plus and minus indicate addition or subtraction. Times indicates multiplication. These keywords help translate verbal descriptions into algebraic function rules.
How do you distinguish the independent from the dependent variable?
The independent variable is what you choose or control. The dependent variable changes as a result. For a rental car problem, miles driven (chosen) is independent, and total cost (result) is dependent.
What textbook covers writing function rules from word problems in Grade 7?
Big Ideas Math Advanced 2, Chapter 6: Functions covers how to write algebraic function rules from real-world word problem descriptions.