Function Notation
Function notation is a Grade 7 math topic from Yoshiwara Intermediate Algebra that introduces the f(x) notation for representing functions. Students learn to read, write, and evaluate functions using this notation, replacing y with f(x) to clearly show the input-output relationship.
Key Concepts
Property We use a letter like $f$ or $g$ to name a function. The notation $f(x)$, read '$f$ of $x$', represents the output value of the function $f$ when the input is $x$. If $y$ is the output variable, we can write $y = f(x)$. The parentheses in $f(x)$ do not indicate multiplication.
Function Notation: Input variable ↓ $f(x) = y$ ↑ Output variable.
Examples Instead of writing 'the area $A$ for a radius $r$ is $\pi r^2$', we can write $A(r) = \pi r^2$. The notation $A(3)$ asks for the area of a circle with a radius of 3.
Common Questions
What is function notation?
Function notation uses f(x) to represent the output of a function f when the input is x. It replaces y in equations, so y = 2x + 1 becomes f(x) = 2x + 1.
How do you evaluate a function using function notation?
Substitute the given input value for x everywhere it appears. For example, if f(x) = 3x - 2, then f(4) = 3(4) - 2 = 10.
Why do we use function notation instead of just y?
Function notation makes it explicit that the value depends on the input x, and it allows you to name multiple different functions (f, g, h) without confusion.
What does f(3) mean?
f(3) means the output of the function f when the input is 3. You substitute x = 3 into the function rule to find the numerical result.