Function Notation
Function Notation is an algebra skill from Openstax Intermediate Algebra 2E, Chapter 3: Graphs and Functions. The notation f(x) names the function f and shows x as the input, with f(x) representing the output or y-value; evaluating the function means substituting a specific value or expression for x and simplifying. This notation is more informative than y = ... because it explicitly identifies the function name and the independent variable.
Key Concepts
Property For the function $y = f(x)$: $$f \quad \text{is the name of the function}$$ $$x \quad \text{is the domain value}$$ $$f(x) \quad \text{is the range value} \quad y \quad \text{corresponding to the value} \quad x$$ We read $f(x)$ as $f$ of $x$ or the value of $f$ at $x$. The process of finding the value of $f(x)$ for a given value of $x$ is called evaluating the function .
Examples For the function $f(x) = 5x 4$, to evaluate $f(3)$, we substitute 3 for $x$: $f(3) = 5(3) 4 = 15 4 = 11$.
For the function $g(x) = x^2 + 2x$, to evaluate $g(a)$, we substitute $a$ for $x$: $g(a) = a^2 + 2a$.
Common Questions
What does f(x) mean in function notation?
f(x) means the output of function f when x is the input; it is read as f of x and represents the y-value corresponding to the input x.
How do you evaluate a function using function notation?
Replace every occurrence of x in the function rule with the given input value or expression, then simplify to find the output.
Does f(x) mean f times x?
No, the parentheses in f(x) do not indicate multiplication; they show that x is the input to the function f.
What textbook covers function notation?
Openstax Intermediate Algebra 2E, Chapter 3: Graphs and Functions introduces function notation and how to evaluate functions.