Introduction to Function Notation

Function notation is a way to represent functions in mathematics. It allows us to express the output of a function based on its input. The standard notation for a function is $f(x)$, where $f$ is the name of the function and $x$ is the input variable.

Explanation

When we see $f(x)$, it means we are evaluating the function $f$ at the input $x$. The output is determined by the rule defined for the function. For example, if we have a function defined as $f(x) = 2x + 3$, this means that for every value of $x$, we can find $f(x)$ by substituting $x$ into the equation.

Worked Example

Let's evaluate the function $f(x) = 2x + 3$ at $x = 4$:

1. Start with the function: $f(x) = 2x + 3$
2. Substitute $x$ with $4$: $f(4) = 2(4) + 3$
3. Calculate $2(4)$: $f(4) = 8 + 3$
4. Add $8$ and $3$: $f(4) = 11$

Thus, $f(4) = 11$.

Key Questions

• What is the value of $f(2)$ if $f(x) = 3x - 1$?
• How do you interpret $g(x) = x^{2} + 5$?
• If $h(x) = 5 - x$, what is $h(3)$?
• What does $f(0)$ represent if $f(x) = 4x + 1$?

Keywords

• Function
• Notation
• Output
• Input
• Evaluation