Understanding Functions in Algebra

A function is a relation that assigns exactly one output value for each input value. Functions are fundamental in algebra and mathematics as a whole.

What is a Function?

A function relates each input to exactly one output.

It is often written as \( f(x) \), where \( x \) is the input.

Domain and Range
  • Domain: The set of all possible input values.
  • Range: The set of all possible output values.
Types of Functions
  • Linear functions: \( f(x) = mx + b \)
  • Quadratic functions: \( f(x) = ax^2 + bx + c \)
  • Polynomial, rational, exponential, and more.
Function Notation

Function notation uses \( f(x) \) to denote the output for input \( x \).

Example: If \( f(x) = 2x + 3 \), then \( f(2) = 7 \).

Practice Problems

  1. Find the domain and range of \( f(x) = x^2 \).
  2. If \( f(x) = 3x - 1 \), what is \( f(4) \)?
  3. Is \( y = \sqrt{x} \) a function?

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