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Basic Polynomial Graphs  Concept
Carl Horowitz
Carl Horowitz
University of Michigan
Runs his own tutoring company
Carl taught upperlevel math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!
Graphing higher degree polynomial functions can be more complicated than graphing linear and a href="/math/algebra/quadraticequationsandfunctions/graphingquadraticequations">quadratic functions. Polynomial graphs can be graphs of functions where the degree of the highest term is greater than one. When we graph polynomials with varying degrees it is easier to identify the end behavior, shape and turning points.
The graphs of some basic polynomials, so for this part we're going to look at the graph of some polynomials and some of these are going to be familiar to you some of them not but we're going to go through the same process just to make sure we understand how we got the basic graphs for all these okay. So right here I have f of x is equal to x okay so you should hopefully recognize this outline but we're going to go through the process just so you see exactly how we get these points. So over here I have a table I have certain values of x and certain values for f of x divide that comes out of it. So if x is negative 2, the same value comes out because f of x is just equal to x so that ends up being negative 2 as well.
All of these values are just going to go in and come out exactly the same. So we end up with negative 1, 0, 1 and 2 okay. These then kind of coordinate correspond to points on the graph okay. So we have negative 2, negative 2 and I'm not going to make my graph exact but just enough so it could give us idea of what exactly is happening. Point a of 2 negative 2, negative 1, negative 1, 0 0, 1 1, 2 2. So we end up with a line slope one passing through the origin. We already knew that from just what we know about lines but going through a process we're able to figure out what this polynomial function looks like.
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Carl Horowitz
B.S. in Mathematics University of Michigan
He knows how to make difficult math concepts easy for everyone to understand. He speaks at a steady pace and his stepbystep explanations are easy to follow.
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Sample Problems (13)
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Basic Polynomial Graphs
Problem 1 4,642 viewsGraph:
f(x) = x² 
Basic Polynomial Graphs
Problem 2 4,326 viewsGraph:
f(x) = x³ 
Basic Polynomial Graphs
Problem 3 4,158 viewsGraph:
f(x) = x⁴ 
Basic Polynomial Graphs
Problem 4 1,295 views 
Basic Polynomial Graphs
Problem 5 1,138 views 
Basic Polynomial Graphs
Problem 6 1,081 views 
Basic Polynomial Graphs
Problem 7 862 views 
Basic Polynomial Graphs
Problem 8 948 views 
Basic Polynomial Graphs
Problem 9 926 views 
Basic Polynomial Graphs
Problem 10 879 views 
Basic Polynomial Graphs
Problem 11 828 views 
Basic Polynomial Graphs
Problem 12 874 views 
Basic Polynomial Graphs
Problem 13 879 views
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