Functions, Domain, and Range
A function is a special relationship where each input value relates to exactly one output value . You can use the vertical line test to identify functions on a graph—if any vertical line crosses the graph more than once, it's not a function.
The domain of a function includes all possible input values that work in the function. The range consists of all possible output values the function can produce. For example, in the function f = √x + 4, the domain is x ≥ -4 because the value inside the square root must be non-negative.
When dealing with fractions like f = 5/, watch out for vertical asymptotes. These occur when the denominator equals zero, making the function undefined at that point. In this case, the domain is all real numbers except x = -5.
💡 Quick Tip: The zeros of a function (where f = 0) are the same as the x-intercepts on its graph. Finding these points helps you understand where the function crosses the x-axis.
