Functions and Graphs ( Beginning Calculus notes), Slides of Mathematics

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Functions and Graphs

Photo by Vickie Kelly, 2006 Greg Kelly, Hanford High School, Richland, Washington

The Parthenon, Centennial Park, Nashville, Tennessee

Domain and Range

Functions have an independent variable (often x ) and a dependent variable (often denoted as aa y ).

domain: The set of all possible x values for a function.

range: The set of all possible y values for a function.

We can find the range by graphing it, and we can see that it does touch 0!

or

Another example:

Find the domain and range of:

Since we cannot take the square root of a negative number, the domain is:

This is a half-open interval.

We use a square bracket on the left boundary point because we count the zero. (The interval is closed at zero.)

When infinity is a boundary, it is always an open interval on that end, with parentheses.

Any function with y-axis symmetry is called an even function.

For example, is an even function.

So is.

This is important in quantum mechanics, when finding a odd solution

A polynomial function with only odd exponents has origin symmetry.

Changing the sign of x changes the sign of y.

In other words, if (x,y) is on the graph, so is (-x,-y).