SOLUTION: Can you determine what the graph of any function looks like just by looking at the function? We've been doing polynomial and rational (polynomial divided by polynomial) functions,

Question 279932: Can you determine what the graph of any function looks like just by looking at the function? We've been doing polynomial and rational (polynomial divided by polynomial) functions, and using the standard procedure for analyzing these functions (i.e. determining the vertical and/or horizontal asymptotes, y-int, x-int, etc.). We haven't done enough of these yet for me to determine what the graph may look like just by looking at it. Maybe seeing how the signs of the terms change, the relative size of the coefficients, the order (power) of the function, or some other property of the function, would allow me to sketch the graph of it without going through the trouble of substituting in points. Often, experienced scholars in a subject can do things like this, but I was wondering if there are tricks or tips for doing this. Thanks! By the way, we haven't done calculus yet, so we don't get to use calculus to figure out how to graph these functions.
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
If by "looks like" you just mean the general shape. Hyperbola parabola ellipse, line, circle.
yes there are standard formulas(equations) for those shapes.

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