Learn what the end behavior of a polynomial is, and how we can find it from the polynomial's equation.
Log in π½πΌπππΌπ 4 years agoPosted 4 years ago. Direct link to π½πΌπππΌπ's post βI'm still so confused, th...β I'm still so confused, this is making no sense to me, can someone explain it to me simply? this is Hard. Thanks! :D β’ (11 votes) obiwan kenobi 4 years agoPosted 4 years ago. Direct link to obiwan kenobi's post βAll polynomials with even...β All polynomials with even degrees will have a the same end behavior as x approaches -β and β. If the value of the coefficient of the term with the greatest degree is positive then that means that the end behavior to β on both sides. If the coefficient is negative, now the end behavior on both sides will be -β. If the polynomials degree is odd, then the end behavior will be different on both sides. If the leading coefficient is positive then the end behavior will be -β as x approaches -β and β as x approaches β. Notice this is from bottom left to top right. If the leading coefficient is negative, the function will now be from top left to bottom right. So its end behavior will be β as x approaches -β and -β as x approaches β. Hope this helps! (35 votes) kyle.davenport 7 years agoPosted 7 years ago. Direct link to kyle.davenport's post βWhat determines the rise ...β What determines the rise and fall of a polynomial β’ (14 votes) Lara ALjameel 6 years agoPosted 6 years ago. Direct link to Lara ALjameel's post βGraphs of polynomials eit...β Graphs of polynomials either "rise to the right" or they "fall to the right", and they either "rise to the left" or they "fall to the left." ... The behavior of a polynomial graph as x goes to infinity or negative infinity is determined by the leading coefficient, which is the coefficient of the highest degree term. 335697 3 years agoPosted 3 years ago. Direct link to 335697's post βOff topic but if I ask a ...β Off topic but if I ask a question will someone answer soon or will it take a few days? β’ (11 votes) Kim Seidel 3 years agoPosted 3 years ago. Direct link to Kim Seidel's post βQuestions are answered by...β Questions are answered by other KA users in their spare time. So, there is no predictable time frame to get a response. Many questions get answered in a day or so. (12 votes) Mellivora capensis 7 years agoPosted 7 years ago. Direct link to Mellivora capensis's post βSo the leading term is th...β So the leading term is the term with the greatest exponent always right? β’ (6 votes) Wayne Clemensen 4 years agoPosted 4 years ago. Direct link to Wayne Clemensen's post βYes. It would be best to ...β Yes. It would be best to put the terms of the polynomial in order from greatest exponent to least exponent before you evaluate the behavior (10 votes) jenniebug1120 7 years agoPosted 7 years ago. Direct link to jenniebug1120's post βWhat if you have a funtio...β What if you have a funtion like f(x)=-3^x? How would you describe the left ends behaviour? β’ (1 vote) Kim Seidel 7 years agoPosted 7 years ago. Direct link to Kim Seidel's post βFYI... you do not have a ...β FYI... you do not have a polynomial function. You have an exponential function. So, you might want to check out the videos on that topic. Related to your specific question... Try some numbers to see what happens. (12 votes) Tori Herrera 4 years agoPosted 4 years ago. Direct link to Tori Herrera's post βHow are the key features ...β How are the key features and behaviors of polynomial functions changed by the introduction of the independent variable in the denominator (dividing by x)? β’ (3 votes) Seth 4 years agoPosted 4 years ago. Direct link to Seth's post βFor polynomials without a...β For polynomials without a constant term, dividing by x will make a new polynomial, with a degree of n-1, that is undefined at 0. For example, xΒ³+2x will become xΒ²+2 for xβ 0. With a constant term, things become a little more interesting, because the new function actually isn't a polynomial anymore. If we divided xΒ²+2 by x, now we have x+(2/x), which has an asymptote at 0. In terms of end behavior, it also will change when you divide by x, because the degree of the polynomial is going from even to odd or odd to even with every division, but the leading coefficient stays the same. (5 votes) perez, dakota 2 years agoPosted 2 years ago. Direct link to perez, dakota's post βHow to not fail? how to d...β How to not fail? how to do? β’ (4 votes) chasephuayoung88 a year agoPosted a year ago. Direct link to chasephuayoung88's post βGo through the lessons, u...β Go through the lessons, understand the content, and show your mastery on tests (2 votes) Katelyn Clark 6 years agoPosted 6 years ago. Direct link to Katelyn Clark's post βThe infinity symbol throw...β The infinity symbol throws me off and I don't think I was ever taught the formula with an infinity symbol. I need so much help with this. I thought that the leading coefficient and the degrees determine if the ends of the graph is... up & down, down & up, up & up, down & down. Thank you for trying to help me understand. β’ (2 votes) Raymond 6 years agoPosted 6 years ago. Direct link to Raymond's post βWell, let's start with a ...β Well, let's start with a positive leading coefficient and an even degree. This would be the graph of x^2, which is up & up, correct? That means that when x increases, y increases. And when x decreases, y still increases. (6 votes) Vaughn 4 months agoPosted 4 months ago. Direct link to Vaughn's post βI feel like this is what ...β I feel like this is what english sounds like to ppl who dont speak it β’ (4 votes) zxczxczxc 2 years agoPosted 2 years ago. Direct link to zxczxczxc's post βI need help I don't under...β I need help I don't understand how to find the end behavior of a fraction. β’ (4 votes) Davey 8 days agoPosted 8 days ago. Direct link to Davey's post βIf you mean a rational fu...β If you mean a rational function(think (x-1)/(x-2), there are a few different ways to do it, all covered in Pre-calculus. Case #1: Degree of numerator > degree of denominator (x^2 - 4x) / (x - 4) x^2/x = x Case #2: Degree of numerator = degree of denominator (x^2 - x) / (2x^2) Case #3: Degree of numerator < degree of denominator (x^2 - x)/(x^3) For the last two cases, you can see they approach one number. This is called a horizontal asymptote. (1 vote)Want to join the conversation?
-3^0 = -1
-3^1 = -3
-3^2 = -9
-3^3 = 27
...etc...
Keep trying some numbers to get a sense of the end behavior.
You can rewrite up & up as xβ+β, f(x)β+β & xβ-β, f(x)β+β.
Same logic goes for the other behaviors.
Here, all you need to do is take the highest-degree term of the numerator & denominator, divide, and then use the method in this article.
x is a positive odd-degree function
Approaches negative infinity at negative infinity, approaches positive infinity at positive infinity
This one is also pretty easy. Again, take the highest-degree monomials and divide:
x^2 / 2x^2 = 1 / 2
The function approache 1/2 at both negative infinity and positive infinity.
This one is really easy. It approache 0 at both negative infinity and positive infinity. Try plotting it on desmos if you need a visual.
