Functions and Their Basics
Think of a function as a super strict rule - for every input x−value, you get exactly one output y−value. No exceptions! It's like having a vending machine where each button gives you only one specific snack.
A function is written as f(x) and represents a set of ordered pairs where no x-value repeats with different y-values. For example, {(1,2), (2,3), (3,4)} is a function, but {(1,6), (2,5), (1,9)} isn't because the x-value "1" appears twice with different outputs.
The domain includes all possible x-values you can plug into your function. Watch out for two danger zones: you can't divide by zero, and you can't take the square root of negative numbers (in this course). For y = √x+4, your domain is x ≥ -4.
The range covers all possible y-values your function can produce. Using that same example, since square roots are never negative, your range is y ≥ 0. The vertical line test is your quick check - if any vertical line crosses the graph more than once, it's not a function!
Pro tip: When finding domain, ask yourself "What x-values would break this function?" Those are the ones to exclude!