Functions are central to algebra, yet many students find them intimidating. The process of working with a function resembles solving a simple equation—such as 2x + 5 = 15—but instead of finding a single solution, you determine a range of possible input and output values.
The domain is the set of all input (x‑values) that a function accepts. These inputs constitute the independent variable.
The range is the set of all output (y‑values) produced by the function for each domain input. These outputs form the dependent variable.
To confirm whether an equation represents a function, examine its coordinate points or graph. For a valid function, each x‑value must correspond to exactly one y‑value. For example, the points (1,2) and (1,3) cannot belong to the same function.
Evaluating a function at a specific x‑value involves substituting that value into the formula. If f(x) = 2x + 1 and you wish to find f(3), calculate:
f(3) = 2(3) + 1 = 7
Thus, the function yields a y‑value of 7 when x = 3.
