End Behavior Quiz Review
end behavior
The behavior of the graph as x approaches positive infinity or negative infinity As x ->+∞, y -> ______ and as x -> -∞, y -> _____
how to find the degree on a given graph
count the x intercepts BE AWARE OF MULTIPLICITIES
how to find the degree of a factored equation
count the x's BE AWARE OF EXPONENTS
End behavior is determined by the...
degree and lead coeffiecient
even multiplicity
graph bounces off the x axis at multiplied point ex: double root
odd multiplicity
graph goes through if x int. appears more than once but still is odd (ex: 3, triple root, line stalls)
multiplicity
how many times the x-int occurs
practice!
https://www.anderson5.net/cms/lib02/SC01001931/Centricity/Domain/2147/Algebra%202%20-%20Polynomials%20-%20End%20Behavior.pdf
what is the end behavior if the degree is odd and the lead coefficient is Positive
opposite directions, Down on left, Up on right (line is positive/increasing) ex. x^3
what is the end behavior if the degree is odd and the lead coefficient is negative
opposite directions, Up on left, Down on right (line is negative/decreasing) ex. -x^3
what is the end behavior if the degree is even but the coefficient is Negative
same directions, both ends down (negative/decreasing) ex. -x^2
what is the end behavior if the degree is Even degree and the lead coefficient is positive
same directions, both ends up (positive/increasing) ex. x^2
how do you find the degree in an equation in standard form
the highest exponent
how do you find the lead coefficient in an equation in standard form
the number in front of the variable with the highest exponent
how do you find a possible equation in factored form to represent a given function
1. put the x intercepts into parentheses ex: if the x int.=2, factor will be (x-2) 2. write the exponents for the x intercepts that were multiplied, like a double or triple root ex: if the x int. of 2 is a triple root, the factor will be (x-2)^3