How do functions, domains, and ranges work?

Question

Trying to figure out some math, I missed the first day of official teaching due to schedule conflicts. I need enough info on these three topics to answer some image-based problems. Thanks!

Answer 1

A function is an expression that has one or no values for each of the allowable input values (those in the domain of the function).  The values produced are called the range of the function.

For example, the function y=2x can be written as  f(x)=2x which is how we often write “f is a function of x.”  The values of x (the independent variable) are the domain of the function and include all real numbers.  The range of the function also include all real numbers.

Another example,

       y = f(x) = x^2

The domain of this function is all real numbers, but the range includes only non-negative real numbers (remember that 0 is neither positive nor negative).

There is what’s called “the vertical line rule.”  That means that if you draw a vertical line along with a graph of y=f(x), there will be either none or one point where the line intersects the funjction.  This is another way of saying that y cannot have two or more values for only one value of x.