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Seven Elementary Functions and Their Graphs - Concept

Teacher/Instructor Norm Prokup
Norm Prokup

Cornell University
PhD. in Mathematics

Norm was 4th at the 2004 USA Weightlifting Nationals! He still trains and competes occasionally, despite his busy schedule.

In math we often encounter certain elementary functions. These elementary functions include rational functions, exponential functions, basic polynomials, absolute values and the square root function. It is important to recognize the graphs of elementary functions, and to be able to graph them ourselves. This will be especially useful when doing transformations.

I want to talk about seven really important functions that I call the parent functions. I've got them graphed here. The first one f of x equals x. This is the identity function. This is sort of the parent of all linear functions. And second, the absolute value function f of x equals absolute value x.
The third, f of x equals x squared, the squaring function, its graph is a parabola and this is the parent of all the quadratic functions. f of x equals x cubed, the cubing function.
Number five, the square root function. f of x equals square root x. A typical exponential function, f of x equals 2 to the x. Notice the difference between 2 to the x and x squared, very different shapes, different classes of function and f of x equals 1 over x the reciprocal function. These are the parent functions, and as we learn how to graph functions in their transformation, we'll use these as our as our sort of chief Guinea pigs. We'll be transforming these and creating new functions out of them and that's why we call them the parent functions. But it's important for you to know these functions. You've probably learned about most of them already if not all of them and just to remember their graphs and know them on sight and also to know key points that the graphs have that that key points that are in the graph the function.
That's it. Those are the seven functions. I will occasionally add to this list as the course goes on.

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