# How do I find the domain and range of these questions? (1 Viewer)

#### DrDawn

##### Member
Can anyone help me out with finding the domain and range of these questions (algebraically, not graphically), any advice or tips is appreciated, thanks so much!

_____________________________________________________________________________________________

Last edited:

#### DrDawn

##### Member
@YonOra could you please offer any advice on how to solve these?

#### dumNerd

##### Well-Known Member
Can anyone help me out with finding the domain and range of these questions (algebraically, not graphically), any advice or tips is appreciated, thanks so much!

View attachment 29635

_____________________________________________________________________________________________

View attachment 29636
For fractions remeber the bottom cannot be 0 or it would be no solution. And for roots the inside has to he bigger than or = 0. These are hints now u can figure it out

#### YonOra

##### Well-Known Member
Cool so, for the domain I like to look at the denominator first. We know nothing can be divided by 0. So for example a), you can see that x =/ -2, and x > -2 also wont work as that'll be a sqr root of a neg No. So now we can say x can be any number greater than or equal to -2. So your domain is x >-2 or x ∈ (-2, ∞).

#### YonOra

##### Well-Known Member
Now the sexy part - algebra.

Take e) for example:
We know that whatever is inside the sqr root must be greater than or equal to 0.
So,
x^2 - 4 ≥ 0
(x-2)(x+2) ≥ 0
Do this whatever way you've been taught to, if you want help, lmk.

Now you have your domain, -2 ≥ x, x ≥ 2.

#### YonOra

##### Well-Known Member
Sorry, I assumed range would be given. For the example above (e)), you can sub in both x values into the equation, and you'll get 0, but you also know that whatever is in the sqr root MUST be positive (because of x^2... i.e. (-1)^2 = 1), therefore we can say R; y ≥ 0

#### DrDawn

##### Member
For fractions remeber the bottom cannot be 0 or it would be no solution. And for roots the inside has to he bigger than or = 0. These are hints now u can figure it out
I understand how to figure out the domain but finding the range is difficult, how do you find it?

#### B1andB2

##### pyjama
I understand how to figure out the domain but finding the range is difficult, how do you find it?
i just draw the graph

#### Trebla

If you’re not too good at inspecting the equation to find the minimum/maximum values of y, then you can use calculus to investigate the nature of turning points.

#### DrDawn

##### Member
Btw does anyone know where I can find more questions like these?

#### YonOra

##### Well-Known Member
Btw does anyone know where I can find more questions like these?
I'll send some over

#### YonOra

##### Well-Known Member
If you’re not too good at inspecting the equation to find the minimum/maximum values of y, then you can use calculus to investigate the nature of turning points.
F.D.T for life

#### DrDawn

##### Member
Also how do you solve for the range when the numerator is x? (for question a)

#### Trebla

Is it not possible to do it algebraically?
Yes, by finding the maximum and minimum turning points, though you’re effectively trying to find the properties of the graph in doing so.

#### DrDawn

##### Member
Yes, by finding the maximum and minimum turning points, though you’re effectively trying to find the properties of the graph in doing so.
I'm so sorry but could you please explain how to find the max and min turning points?

#### DrDawn

##### Member
Ok so basically you have to draw a rough sketch of the graph to find the range (or alternatively you can do calculus), and for domain you can find it by solving the equation in the denominator (thus finding the asymptotes and domain)

#### Trebla

Ok so basically you have to draw a rough sketch of the graph to find the range (or alternatively you can do calculus), and for domain you can find it by solving the equation in the denominator (thus finding the asymptotes and domain)
It’s better to think of these as “tools” you could potentially use rather than as prescribed methods. Techniques like “solving the equation of the denominator” don’t work if the function doesn’t have a denominator to solve in the first place!

At the end of the day your goal is just to find the all the allowable x values and allowable y values for a function. There are many ways to go about doing that and some techniques only work for specific types of functions.

#### DrDawn

##### Member
And yes, I do agree with Trebla above, that it’s better to think of these as “tools” you could potentially use rather than as prescribed methods.
However, I do understand that some people prefer to learn with a clear method, and if that's what you want to use, that should be fine too!
I don't want to use those tools too often because it only works for certain equations so what would be a "clear" method to solve these?