Consider the leading term of the polynomial function. What is the end behavior of the graph? Describe the end behavior and provide the leading term.
-3x5 + 9x4 + 5x3 + 3
1= quintic
2= -8x^5+10x^4
3= down and up
4= there are two turning points
5= x=0,x=2,x=-3 (Meets at 8 on top)
Enjoyy!! Merry x-mas!!🎄
Jewel right but to help on the graphs this may help
1.A-quintic
2.B-8x^5+10x^4
3.C-down and up (look at end of sentence)
4.A-there are two turning points
5.A-x=0,x=2,x=-3 (Meets at 8 on top)
Up and down
To determine the end behavior of the graph, we need to examine the leading term of the polynomial function.
The leading term is the term with the highest degree in the polynomial. In this case, the leading term is -3x^5.
The degree of a term represents the highest power of the variable within that term. In this case, the degree of the leading term is 5.
When the degree of the leading term is odd (in this case, 5), the end behavior of the graph is as follows:
- If the leading coefficient (in this case, -3) is positive, the graph will rise on both ends.
- If the leading coefficient is negative, the graph will fall on both ends.
Therefore, the end behavior of the graph of the polynomial function -3x^5 + 9x^4 + 5x^3 + 3 can be described as follows:
As x approaches negative infinity, the graph rises indefinitely.
As x approaches positive infinity, the graph also rises indefinitely.
So, the end behavior of the graph is an upward trend on both ends.
To summarize:
End behavior: The graph rises indefinitely on both ends.
Leading term: -3x^5
the leading term has the greatest exponent ... 5 in this case
... you should use the "caret" symbol (^) for exponentiation
5 is odd, so the behavior at the positive and negative ends of the graph are opposite
a large negative x value causes the function to have a large positive value
... this is due to the negative coefficient of the 1st term
the opposite can be said of a large positive x value