Math Is Fun Forum

mathland

Member

Registered: 2021-03-25

Posts: 444

Find Range Algebraically

I think the easiest way to find the range of functions that are not linear is to make a graph. Yes? What if I wanted to find the range without graphing? See below.

Find the range of each non-linear function below.

1. f(x) = (x + 2)/[sqrt{x - 10}]

2. f(x) = [sqrt{x + 6}]/(6 + x)

How is this done algebraically?

Note: sqrt = square root

Bob

Administrator

Registered: 2010-06-20

Posts: 10,619

Re: Find Range Algebraically

All the things I would do are part of creating the graph.  I cannot think of leaving that out.

You can differentiate to finds stationary points and look for asymptotes.  Set x = 0 and y = 0. Let x tend to + / - infinity.

But in the end I would use all that to make a graph.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathland

Member

Registered: 2021-03-25

Posts: 444

Re: Find Range Algebraically

All the things I would do are part of creating the graph.  I cannot think of leaving that out.

You can differentiate to finds stationary points and look for asymptotes.  Set x = 0 and y = 0. Let x tend to + / - infinity.

But in the end I would use all that to make a graph.

Bob

In other words, graphing is the best approach to find the range. After graphing this function, what should I be looking for to find the range in the picture? Also, the range is the y-coordinate of the point (x, y). If so, then I am searching for the height of the graph. Yes?

Do you sleep? The time in NYC is 4:28 am. I am currently on lunch break as I work overnight hours. I have a reason to be up now. Why are you up this time? Just curious....