Find domain and range of function

One skill students have have trouble with is how to find the domain and range of a function. Recall that a function is a "rule" that takes each input to one output. All the possible inputs constitute the domain and the set of all possible outputs is the range. What we need to do to find the domain and range depends on how the function is presented to us. If we are given a symbolic representation (ie, a formula), then we start by assuming that the domain is all real numbers. We then check for "trouble makers" and remove them from the domain. Trouble makers will be values that if we were to pull them into the function, undesirable outcomes would occur, such as dividing by '0'. The two principle types of problems which might occur are division by zero and taking the square root (or any even root) of a negative. The available handout has several nice examples of the checks you should preform when you want to find the domain of a function. If we are given a graphical representation of a function, then we can read the domain and range right of the graph. This can be done by "squashing" the graph down to the x- and y-axis. When we smash the graph down to the x-axis, all x values that are covered are part of the domain. If we squash the graph horizontally on to the y-axis, then the covered y values become the range.

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