Without evaluating, determine if each expression will be positive or negative.
Consider
What happens to the y-values as the x-values get bigger and bigger? Try a few values to investigate.
What happens to the y-values as the x-values decrease without bound? Try a few values to investigate.
Consider
What happens to the y-values as the x-values get bigger and bigger? Try a few values to investigate.
What happens to the y-values as the x-values decrease without bound? Try a few values to investigate.
How would your answers to numbers 8 and 9 change if the function was
The graphs of the functions
Compare the end behavior of the two graphs.
Which term in the polynomial seems to have the biggest impact on the end behavior of the graph?
Why do you think this is?
Right end behavior comes from whether the function is positive or negative (determined by the leading term.)
Positive: ____________ ↑
Negative: ___________ ↓
Then the degree fills in the left end behavior
Even degree's left end behavior has the same as the right end behavior.
Odd degree's left end behavior has the opposite of the right end behavior.
In Algebra, we mainly used ↑↑, ↓↑, ↑↓, and ↓↓.
But for Precalculus, we will discuss the limits.
and
and
and
and
↑↑
↓↑
↑↓
↓↓
Use limit notation to describe the end behavior of the graph shown.
Is it possible for this graph to have a degree of 5? Why or why not?
Which of the following terms, when added to the given polynomial, will change the end behavior? Check all that apply.
Use limit notation to describe the end behavior of
The graph of
