Section 4.2: Function Notation

Function notation provides a convenient way to name a function and show the input-output relationship.

Function Notation:

If \( f \) is a function, then \( f(x) \) represents the output corresponding to input \( x \).

Example: \( f(x) = 2x + 3 \), then \( f(1) = 2(1) + 3 = 5 \).

Example 1

Given \( f(x) = 3x - 4 \), find \( f(2) \) and \( f(-1) \).

\( f(2) = 3(2) - 4 = 2 \)

\( f(-1) = 3(-1) - 4 = -7 \)

Evaluate \( g(x) = x^2 + 5 \) for \( x = 0, 3, -2 \).

\( g(0) = 0^2 + 5 = 5 \)

\( g(3) = 9 + 5 = 14 \)

\( g(-2) = 4 + 5 = 9 \)

For \( f(x) = 4x + 1 \), find \( f(3) \) and \( f(-2) \).
For \( h(x) = x^2 - 2x \), find \( h(0) \) and \( h(5) \).
Given \( k(x) = 2x + 7 \), determine if \( k(3) = 13 \) is correct.
Write a function rule for a function that doubles the input and adds 1.
Evaluate \( f(x) = x^3 - x \) for \( x = 2 \) and \( x = -1 \).