What is an example of a function?

Hello! As a domain expert in mathematics, I'm glad to help you understand what a function is and provide an example. A function is a mathematical concept that describes a relationship between two sets of elements. The first set is known as the domain, and the second set is called the codomain. The function maps each element from the domain to a unique element in the codomain. This mapping is defined by a set of ordered pairs, where the first element of each pair is from the domain, and the second element is from the codomain. It's important to note that not all elements in the codomain need to be an output of the function; they are merely the possible outputs. Let's look at a simple example of a function. Consider the function \( f(x) = x^2 \), where \( x \) is a real number. This function takes an input from the set of all real numbers (the domain) and maps it to the set of all non-negative real numbers (the codomain). For every real number \( x \), there is a unique output \( x^2 \), which is always non-negative. Here's a step-by-step breakdown of how this function works: 1. Choose an Input: Select a real number to be the input for the function. Let's say we choose \( x = 3 \). 2. Apply the Rule: The rule for our function is to square the input. So, we calculate \( 3^2 \). 3. Get the Output: The result of \( 3^2 \) is \( 9 \), which is the output for our function with the input \( x = 3 \). This process can be repeated for any real number. For instance, if we choose \( x = -2 \), the output would be \( (-2)^2 = 4 \), and if \( x = 0 \), the output would be \( 0^2 = 0 \). It's also worth mentioning that functions can be represented in various ways, including: - Graphically: as a curve on a graph, where the x-axis represents the domain and the y-axis represents the codomain. - Numerically: as a table of values. - Algebraically: as an explicit formula, like \( f(x) = x^2 \). - Verbally: in words describing the relationship between the input and output. Now, let's move on to the next steps as per your instructions.

Function examples. A function is a mapping from a set of inputs (the domain) to a set of possible outputs (the codomain). The definition of a function is based on a set of ordered pairs, where the first element in each pair is from the domain and the second is from the codomain.