How do you find the domain and range of a function without the graph

Mathematics

1 answer:

Ber [7]3 years ago

5 0

Hello!

With some functions, there are a few ways to find the domain and range without a graph. One key way to find numbers that are not part of the domain is to look for undetermined numbers, such as x/0. Numbers like these are undetermined. You could also look for numbers that the function could accept, such as having a certain input be equal to a certain output or range, which isn't as common but can still be helpful in some situations.

I hope this helps!

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If y = 10x - 1 and the value of x is 10, what is the value of y?

KatRina [158]

Answer:

Step-by-step explanation:

99 because x= 10 so 10 times 10 is 100 - 1 will = 99

5 0

3 years ago

Multiply 3/sqrt17- sqrt2 by which fraction will produce an equivalent fraction with rational denominator

zzz [600]

Answer:

Step-by-step explanation:

To simplify something that looks like $\frac{\text{whatever}}{\sqrt{a}-\sqrt{b}}$ you would multiply the top and bottom by the conjugate of the bottom. So you multiply the top and bottom for this problem I just made by:

$\sqrt{a}+\sqrt{b}$ .

If you had $\frac{\text{whatever}}{\sqrt{a}+\sqrt{b}}$ , then you would multiply top and bottom the conjugate of $\sqrt{a}+\sqrt{b}$ which is $\sqrt{a}-\sqrt{b}$ .

The conjugate of a+b is a-b.

These have a term for it because when you multiply them something special happens. The middle terms cancel so you only have to really multiply the first terms and the last terms.

Let's see:

(a+b)(a-b)

I'm going to use foil:

First: a(a)=a^2

Outer: a(-b)=-ab

Inner: b(a)=ab

Last: b(-b)=-b^2

--------------------------Adding.

a^2-b^2

See -ab+ab canceled so all you had to do was the "first" and "last" of foil.

This would get rid of square roots if a and b had them because they are being squared.

Anyways the conjugate of $\sqrt{17}-\sqrt{2}$ is