Question

A function can be expressed algebraically such as f(x) = 3x +1, list two forms that a function can be expressed in

Answer 1

Functions can be expressed in several forms. Here are two common forms:

1. **Algebraic Form**: This includes equations like the one you provided, such as \( f(x) = 3x + 1 \). This form represents the function using algebraic expressions.

2. **Graphical Form**: This represents the function visually, typically as a graph on a coordinate plane. For the function \( f(x) = 3x + 1 \), the graph would be a straight line with a slope of 3 and a y-intercept of 1.

Other forms include:

3. **Tabular Form**: A table showing input values (x) and corresponding output values (f(x)).

4. **Set-builder Form**: This specifies a function as a set of ordered pairs, typically in the form \( \{(x, f(x)) | x \in D\} \), where \( D \) is the domain of the function.

Each form serves a different purpose depending on the context in which the function needs to be analyzed or utilized.