##### Like what you saw?

##### Create FREE Account and:

- Watch all FREE content in 21 subjects(388 videos for 23 hours)
- FREE advice on how to get better grades at school from an expert
- FREE study tips and eBooks on various topics

# Seven Elementary Functions and Their Graphs - Concept

###### 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.

Please enter your name.

Are you sure you want to delete this comment?

###### Norm Prokup

PhD. in Mathematics, University of Rhode Island

B.S. in Mechanical Engineering, Cornell University

He uses really creative examples for explaining tough concepts and illustrates them perfectly on the whiteboard. It's impossible to get lost during his lessons.

Thiswas EXCELLENT! I am a math teacher and have been looking for an easy/logical way to explain the lateral area of a cone to my students and this was incredibly helpful, thank you very much!”

I just learned more In 3 minutes of polygons here than I do in 3 weeks in my math class”

Hahaha, his examples are the same problems of my math HW!”

#### Related Topics

- Graphing the Transformation y = f(x - h) 20,640 views
- Domain Restrictions and Functions Defined Piecewise 29,410 views
- The Reflection y = f(-x) 15,358 views
- Symmetry of Graphs: Odd and Even Functions 19,454 views
- The Greatest Integer Function 29,404 views
- The Transformation y = f(bx) 10,455 views
- Computing Difference Quotients 26,173 views
- Finding the Domain of a Function 30,402 views
- Graphing the Transformation y = a f(x) + k 26,600 views

## Comments (0)

Please Sign in or Sign up to add your comment.

## ·

Delete