Question

A function definition has what two parts?

Short answer

Based on the step-by-step solution provided, answer the following question: Question: Identify and describe the two main parts of a function definition using the example function h(x) = 5x - 7. Answer: The two main parts of a function definition are the function name (and parameters) and the function rule (or expression). In the example function h(x) = 5x - 7, the function name is "h" and the parameter is "x". The function rule, or expression, is "5x - 7", which means we need to multiply the input (x) by 5 and then subtract 7 to obtain the output.

Step-by-step solution

Introduction to functions

A function is a relation between a set of inputs and a set of possible outputs, where each input is related to exactly one output. Functions are used to model relationships between different quantities, and they are generally defined by a rule that determines the output for a given input.

Part 1: Function Name (and parameters)

The first part of a function definition is the name of the function, which is typically represented by a single letter (e.g., f), and the parameters (inputs) of the function, which are enclosed in parentheses. For example, consider the function f(x) where x is the input. The name of the function is "f", and "x" is the parameter.

Part 2: Function rule (or expression)

The second part of a function definition is the rule or expression that tells us how to calculate the output for any given input. This rule is often represented by a mathematical formula that involves the input parameter(s). For example, the function f(x) = 2x + 3 describes a relationship between an input x and its corresponding output. The rule for calculating the output is to multiply the input by 2 and then add 3.

Example of a function definition

Let's consider a simple example to illustrate both parts of a function definition. Suppose we have a function g(x) that calculates the square of a number x. The function definition would be: g(x) = x^2 Here, "g" is the name of the function, "x" is the parameter, and the rule is "x^2", which means that we need to square the input (x) to obtain the output.