f(x) means function of x and then this function is defined by using the equals sign: f(x)=2|x|, where x is the independent variable and the subject of the function. Here we have y=f(x) where y is the dependent variable because it depends on x. Using y means we can graph the function using x and y axes. All the possible values for x are called the domain, or the domain of x. So what are the constraints on the values of x? It seems x can be any number from minus infinity to plus infinity. The range is the range of values y or f(x) can take. The absolute value implied by the vertical bars means that the range will be restricted because all the negative values of x will produce a positive value for f(x). The smallest value is when x=0, when y=0. The graph looks like a straight line starting at the origin and inclined at an angle of 45 degrees as it heads to the right. The y axis is like a mirror and reflects the right-hand image so on the left the line starts at the origin and heads off to the right at 45 degrees. The graph looks like a wide V.
y=|x| expresses a relationship between the variables x and y. Also, for each x there is one and only one value for y. The relation between x and y transforms each x point to a corresponding y point. In this case apart from x=0, two x points are mapped to the same y point. For example, x=1 and x=-1 both map, or are transformed, to the point y=1. If all the possible values of x are represented by the contents of a circle and all the possible values of y are similarly represented by a different circle then f is the function that takes each x point in the x circle (domain) and carries it over to the y circle. So we would see two mapping lines from x converging to a single y (apart from x=0). The y circle would contain no negative values.