Question

Please find the function rule

Answer 1

Functions are usually represented by a function rule where you express the dependent variable, y, in terms of the independent variable, x.

y=2.50⋅xy=2.50⋅x

You can represent your function by making it into a graph. The easiest way to make a graph is to begin by making a table containing inputs and their corresponding outputs. Again we use the example with the carrots

Input, x (lb)Output, y ($)0012.5025.0037.50

A pair of an input value and its corresponding output value is called an ordered pair and can be written as (a, b). In an ordered pair the first number, the input a, corresponds to the horizontal axis and the second number, the output b, corresponds to the vertical axis.

We can thus write our values as ordered pairs

(0, 0) - This ordered pair is also referred to as the origin
(1, 2.5)
(2, 5)
(3, 7.5)

These ordered pairs can then be plotted into a graph.

A pairing of any set of inputs with their corresponding outputs is called a relation. Every function is a relation, but not all relations are functions. In the example above with the carrots every input gives exactly one output which qualifies it as a function.

If you are insecure whether your relation is a function or not you can draw a vertical line right through your graph. If the relation is not a function the graph contains at least two points with the same x-coordinate but with different y-coordinates.

The relation portrayed in the graph to the left shows a function whereas the relation in the graph to the right is not a function since the vertical line is crossing the graph in two points.