For a function f(x)=y :

The Domain is all the values x is allowed to be.

The Range is all the values y can be, considering all allowed x.

For example: f(x)=1/(x²) has a Domain of "x is not equal to 0" (since it would be undefined due to division by zero) and a Range of y > 0 since no value of x gives a negative or zero value from the function, but you can get any positive real number result you want.

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None of those require a calculator. Domain and range can be found by observing the function and it's inverse and finding out the points where it isn't defined. Exclude those points and you get the domain and range. Asymptotes are basically those points you excluded while finding the domain and range. x intercept is the point where y = 0 and y intercept is the point where x = 0. For any given question, all these barely takes 2-3 minutes with good practice. More on reddit.com

Change f(x) to y and it should work More on reddit.com

The punchline of first semester calculus is this: You learn a formula to find the slope of a function (well, of the tangent line) at a point. The slope at the top of a hill/bottom of a valley is 0. Set slope to 0 to find the tops and bottoms of things. (Maximize profit, etc.) Before that though, you learn about continuous functions (you can draw them without lifting your pen). So for range, you take a continuous chunk of that graph (e.g. y=1/x has two chunks), find it's top and bottom, and now you know the range for that chunk. Combine all the ranges (there might only be one chunk), and you have the range for the function. The calc kids are right. A lot of things get easier once you know calc. It's called precal for a reason. It's not its own subject, just prep for calc. More on reddit.com