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### Course: Algebra (all content)>Unit 10

Lesson 34: End behavior of polynomial functions

# End behavior of functions & their graphs

Sal picks a function that has a given end behavior based on its graph. Created by Sal Khan.

## Want to join the conversation?

• @ Can you have several local Maximum and minimum points in a function?
• Yes. There are some videos on the site about local minimum and maximum points. Local minimums and maximums happen when you have wavy-looking functions. The bottoms and tops of the waves would all be local minimums and maximums.
• at , what is a "local minimum/maximum" point versus a "global minimum/maximum" point?
• A local minimum is a point where changing `x` by a tiny amount in either direction causes `f(x)` to increase. However, there can be an unlimited number of local minimums, and in between each pair of local minimums there is a local maximum. However there can be only one global minimum, which is the uniquely lowest point the function ever returns.
• f(x) does seem to be increasing as x increases, but at any point will the graph become vertical?
• At Sal mention local minimum and maximum points and later global maximum points. What do these mean?
Did he do a video on it? Can you please explain to me what they mean by local and global and maximum and minimum points?
Thanks.
• Is trigonometry harder or precalculus? (Just curious. I moved to US not long ago.) :)
(1 vote)
• Trig is a subset of precalculus, so precalculus would be harder by definition.
• How can you tell witch way the lines are moving or do you not need to know that?
• You can say that the lines move both ways. The graphs shown are all continuous and have domains of all reals. In other words, any x value, no matter how large or small, can be put into the functions and a y value can be found.
(1 vote)
• How do we calculate the turning point exactly?
Example: (0,9)
• I came across a question asking me if a function was periodic.
What does this mean?
• Function f(x) is periodic if and only if:
f(x + P) = f(x)
Where P is a nonzero constant (commonly referred to as the fundamental period).
A periodic function is basically a function that repeats after certain gap like waves. For example, the cosine and sine functions (i.e. f(x) = cos(x) and f(x) = sin(x)) are both periodic since their graph is wavelike and it repeats. On the other hand, f(x) = x (the parent linear function) graphs a simple line and there is no evident repeating pattern in its graph and upon analyzing the domain of the function we see that it does not satisfy the property f(x + P) = f(x). Therefore we say this function is aperiodic.
(1 vote)
• Also can there be more than one local minimum and maximum local points in one function?
(1 vote)
• Yes, you can have any number of local max or min in a function (though for polynomials there are set numbers of each that you can have).