describe the similarities and differences between y=x^2 and a power funtion with a even degree higher than two?
please help me!!!
You must have patience. Tutors volunteer their time to answer questions.
Maybe a tutor that is familiar with you question isn't on right now.
Reposting the same question over and over will not get an answer any sooner.
Also, if you look at one of your prior posts someone did answer your question.
yes i saw the answer,i didn't want to reply back and say that wasn't what the question was asking b/c that would sound to mean. so i reposted it.
yes i saw the answer,i didn't want to reply back and say that wasn't what the question was asking b/c that would sound to mean. so i reposted it.
It will not sound mean if you explain why the answer did not suit your needs. This is part of communication. You want to be a good mathematician (or any other profession), but you always need to communicate with others. This is where you would get the practice.
In fact, the given answer was all valid, perhaps not as detailed as you wish, and not directly suitable for your assignment.
I suggest you read your (I believe) previous post on "advanced functions" about odd powers and the line y=x. The format of the reply is exactly the same, just a few changes are required to adapt to even powers and y=x².
Post your proposed answer for even functions and we'll be more than pleased to review it.
Here's the link for the previous similar post:
http://www.jiskha.com/display.cgi?id=1297211421
Also, here's is a plot of x^6 and x^2, but it doesn't show up very well because of the enormous difference in scale. However, I am sure you already know what a parabola (x^2) looks like.
http://img130.imageshack.us/i/1297297572.png/
Finally, I just want to add a word that reposting does not help getting your answers faster, simply because more tutors will look through posts that they have looked at before. This is time they could be responding to posts. So in fact, you are slowing down the system by reposting. On the other hand, if the post remains unanswered after 6-12 hours, reposting is OK, and it is preferable to mark repost on the subject line.
Thank you for your kind cooperation.
i wrote that the domain and range were the same for even funnctions. i wrote that they both share the vetical relfection charcetsitc, and the end behavior. by the way my teaher doesnt like saying from quadrant 1 to 2 for end behaviour is there another way of saying it? theay both have similar shapes.
differnces
i wrote that there is none. i toke the exaple y=x^2 and y= x^4. i didntsee anyother differenceexcept that y= x^4 seemed to be streched. is there more i can write for differences?
Quite well done!
You can add a couple more if you wish.
similarities: (in addition to yours)
Both have no singularities.
Both are even functions (=> reflexion about the y-axis)
Both pass through (0,0) which is the only zero of the function.
Both have an absolute minimum at (0,0).
Both have no local or global maximum.
Both are concave upwards on ℝ.
Both are strictly decreasing from -∞ to 0, and strictly increasing from 0 to ∞.
Both are surjective ("onto", i.e. there is an x for every y in the codomain).
Differences:
x^4 increases much faster than x^2.
x^4 is "flatter" than x^2 on the interval [-1,1].
The difference is shape is more pronounced if the x^4 function were a polynomial with more terms, which will cause more maxima and minima, and the shape is generally described as a "W".
Sure, I'd be happy to help explain the similarities and differences between the quadratic function y = x^2 and a power function with an even degree higher than two.
Similarities:
1. Both functions are power functions, meaning they are of the form y = ax^n, where a is the coefficient and n represents the degree.
2. Both functions belong to the class of functions known as polynomial functions, which means they are made up of terms that involve only powers of x.
Differences:
1. Degree: The quadratic function y = x^2 has a degree of 2 because the highest power of x is 2. However, a power function with an even degree higher than two would have a degree greater than 2. For example, y = x^4 has a degree of 4 because the highest power of x is 4.
2. Shape of graph: The quadratic function y = x^2 represents a parabola, which has a symmetric U-shape, and opens upwards if the coefficient "a" is positive. On the other hand, a power function with an even degree higher than two would have a more complex shape, which may have multiple turning points and can look quite different from a simple U-shaped parabola.
3. Rate of change: The rate of change of a quadratic function y = x^2 increases steadily as x moves away from zero and gets steeper, whereas the rate of change of a power function with an even degree higher than two can be more varied and depend on the specific value of the exponent.
4. Intercepts: The quadratic function y = x^2 intersects the y-axis at the origin (0,0) and does not intersect the x-axis. A power function with an even degree higher than two could intersect the y-axis at different points depending on the value of the coefficient "a," and it may have multiple x-intercepts.
To understand these similarities and differences, it is helpful to graph the functions or use critical thinking skills. Graphing calculators or software like Desmos or Wolfram Alpha can plot these functions and help visualize the similarities and differences numerically and graphically.