# Precalculus (MATH-1300)

This course is basically a combination of College Algebra and Trigonometry. The course will have a great emphasis on functions. While you should have seen that concept before, you may not have concentrated on it very much. Now you will.

An expression like 3x + 2 literally stands for a real number; you simply don't know which number until you know which number the variable x stands for. But when we work with that expression, we often think about all of the values that it can take, as x varies, at once. For example, to graph that expression, we don't just draw a point (for a single value) or even really a bunch of points; we draw a line. Geometrically, that line is itself a single complete object in its own right, something more than a point. Algebraically, we can also think of an expression as describing a single complete object in its own right, something more than a number. That something is a function.

Much as we can write the solution set of an inequality as, for example, {x | x < 3}, so we can also write a function as, for example, (x ↦ 3x + 2). However, for historical reasons, that notation is not used in most Algebra books. Instead, it is common to give a function a name, just as we might give the value of an expression a name in a word problem, and there is special notation for that. If f stands for our function, then instead of writing f = (x ↦ 3x + 2), we write f(x) = 3x + 2 (stating it for all values of x), which means the same thing. This is convenient notation anyway, because with it we can calculate, for example, that f(5) = 3(5) + 2 = 17. (Remember that, while x here stands for a number, f stands for a function, which is not the same type of thing. So, 3(5) means 3 times 5, and even x(5) would mean x times 5, but f(5) does not work like that.)

Of course, we will also do more of solving equations, graphing expressions, applying Algebra in word problems, and everything else that's a part of Algebra. In particular, we will look at these with exponential, logarithmic, and trigonometric operations; that is, we will look at expressions like 2x (where x is allowed to be any real number, not just a rational number), log2x, and sin x. (If you don't know what those mean yet, that's OK; we'll cover that!)

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This web page was written by Toby Bartels, last edited on 2021 August 23. Toby reserves no legal rights to it.

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