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