Question

Is y=1/2x-6 a function? Explain please.

Answer 1

Yes this is a function

Explanation:

Any single value of `x` has only 1 value of `y`

`color(blue)("Added note")`
Convention is that the horizontal axis is the independent variable. That is, it can take any value you so wish. The vertical axis is the dependant variable (answer).

There is something that is sometimes referred to as 'the vertical test'

If there is any point at all where a vertical line cuts the plot by more than once then it is not a function.

A quadratic is such that any vertical line only has 1 y-value related to the relevant x-value. So it is a function.

A circle on the other hand will have a group of x-values (domain) that has 2 values for y. Thus by the criterion of the vertical rule it is not a function.

Extract from Collins Dictionary of Mathematics:

A relation between two sets that associate a unique element of the second with each of the first.....

Translation by me:
The first set`->` say, all the x-axis values
The second set`->` the y-axis

any single x-value is related to a unique y-value (just 1 of them)
You can have several x-values that relate to 1 y-value which is still ok as long as any particular x-value only relates to 1 y-value.

This is called a 'many-to-one' relationship