How to find the range of a function?

To find the range, you need to have some idea of what the graph will look like. Example: y=x
You know that the domain is the element of real numbers. Looking at the graph of this function, you should know it is a straight vertical line. The y values are able to take on all value therefore the range is also the element of real numbers.

Say you have a slightly harder function y=x^2+2 This is a quadratic graph that has been shifted upwards by two (because of the +2). Looking at the y values for the range, you can see that the y values do not go below 2. They do, however, go to any value above 2. Therefore the range of this function would be y is an element of real numbers, y is bigger or equal to 2.

y∈R | y≥2

Assuming this is in calculus the minima and maxima can be discovered using the derivative of the function. Where the derivative is positive the function is increasing and and where the derivative is negative the function is decreasing. Extrema can be found where the derivative is 0. If the derivative has no more zeros than the function will continue to increase or decrease infinitely. Prior to calculus finding the range of a function is more of a logical exercise.

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