Question

I am having problems finding the range of a function. I know how to see it graphing but solving by hand has been an issue.. How exactly do I find the range of say.. 8/2x2+5 (its 2xsquared) not sure how to show

Answer 1

So range is all about the different values that y can be. I'd start by making a number line. Y is always going to be positive since the X is squared in the equation. First lets look at when x = 0, you get 8/5, now lets look at when X approaches positive infinity, you get a 8 over infinity since the denominator would always be increasing, thus it equals 0. Therefore, the range for the function is 0 < y <= 8/5. Hope this helps!

Answer 2

Well they wanted us to do this with out graphing. Its college calculus and the way the professor did it in class wasdone out a lot. Sort of solving for something..

Answer 3

Well it's not really graphing so much as just thinking it through in terms of a number line. There is no real algebraic method for solving for range, because you have to consider all the y values in terms of all the x values. Does the prof want work to be shown?

Answer 4

Yes they want work to be shown

Answer 5

So if it was the other way around it was be \[\left[ 8/5,\infty \right]\]