Chapter 1
Numbers and Operations
Course: Gace Middle Grades Math 4 8 704
Subject: Gace Middle Grades Math 4 8 704
Chapter: Functions
1. Interprets statements that use function notation in terms of a context
Function notation f(x) emphasizes the functional relationship between an input (x) and an output. It allows precise communication of how one variable depends on another.
Steps to interpret function notation:
- Identify what the independent variable x represents in the scenario (time, quantity, distance, etc.).
- Identify what the dependent variable f(x) represents (cost, height, population, etc.).
- Substitute values into the function to extract specific information.
Examples:
- If P(t) = 1200(0.97)^t represents the price of a machine t years after purchase, then P(5) = 1200(0.97)^5 ≈ 1036 means after 5 years the machine is worth about $1036.
- If W(h) = 150h models the number of words typed after h hours at a constant rate, then W(2.5) = 375 means 375 words are typed in 2.5 hours.
- If S(t) = 10t² represents the distance fallen in meters after t seconds, then S(3) = 90 means the object has fallen 90 meters in 3 seconds.