End Behavior - Mason Wang by Mason Wang https://padlet.com/22mw07791/gugurmm1no08 Stuff on end behaviors for polynomial functions en-us 2017-12-12 23:27:27 UTC 2025-10-25 14:02:49 UTC hello@padlet.com What is End Behavior? 22mw07791 https://padlet.com/22mw07791/gugurmm1no08/wish/215643814 The end behavior of a function describes the trend of the graph if we look to the right end, as x approaches infinity, and the left end, as x approaches -infinity, does the y-value approach infinity or negative infinity?]]> 2017-12-12 23:28:39 UTC https://padlet.com/22mw07791/gugurmm1no08/wish/215643814 How can the monomial with the highest degree in the polynomial affect the end behavior? 22mw07791 https://padlet.com/22mw07791/gugurmm1no08/wish/215644057 The monomial with the highest degree in the polynomial affects the polynomial's end behavior. Letting f(x) be an arbitrary polynomial function, we write f(x) = g(x) + h(x), where g(x) is its highest-degree term while h(x) is the rest of the function. The graph of f(x) clearly follows the trend of g(x) at the "ends" of the graph, where the "ends" represent the values of x where x is large(approaches infinity) and very small(approaches negative infinity). ]]> 2017-12-12 23:32:08 UTC https://padlet.com/22mw07791/gugurmm1no08/wish/215644057 How to determine the End behavior of a polynomial function 22mw07791 https://padlet.com/22mw07791/gugurmm1no08/wish/215644290 First, you find the coefficient and degree the highest degree monomial in the polynomial function. Let us call that a*x^n.
Now, there are four cases.

1. a is positive, n is odd -> the end behavior is then falling left, rising right

2. a is positive, n is even -> the end behavior is rising left, rising right

3. a is negative, n is odd -> the end behavior is rising left, falling right

4. a is negative, n is even -> the end behavior is falling left, falling right. ]]> 2017-12-12 23:35:27 UTC https://padlet.com/22mw07791/gugurmm1no08/wish/215644290 How do we know? 22mw07791 https://padlet.com/22mw07791/gugurmm1no08/wish/215644527 Well, all functions of the form x^2n all have an end behavior of rising left rising right, and when the a value is negative, it is reflected over the x-axis, so when a is negative and n is even the end behavior is falling left and falling right.

Similarly, all functions of the form x^2n+1 has the end behavior of falling left rising right, so when a is negative, it is reflected over the x-axis, so the end behavior when a is negative and n is odd is rising left falling right. ]]> 2017-12-12 23:38:19 UTC https://padlet.com/22mw07791/gugurmm1no08/wish/215644527