Question

why is the function f(x)=4x+2 a legitimate function? ill give a medal:)

Answer 1

For it to be a function for each value of x there can be one and only one value for f(x).

Answer 2

is that why this function is legitimate?

Answer 3

That is what makes a function a function

Answer 4

but why is f(x)=4x+2 a function? like I have to explain why that is a function

Answer 5

Yes, basically, if it passes the vertical line test, then it is a function. The vertical line test is just use your finger and go across the graph, if any 2 points line up, then it is not a legitimate function:

Answer 6

In your case, it will be:
This passes the vertical line test, so it is a function. What the vertical line test is, is that it checks if any x value has the same y value; what @nelsonjedi .