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