# What is the domain and range of y=2 all over x-3? Thank you

Jun 25, 2018

domain $\to \left\{x : x \in \mathbb{R} , x \ne 3\right\}$
range $\textcolor{w h i t e}{\text{d}} \to \left\{y : y = 2\right\}$

#### Explanation:

Formatting help: Take a look at https://socratic.org/help/symbols. I would suggest that you book mark this page for futor reference.

Notice the hash symbols at the beginning and end of the entered mathematical expression example. This signal the start and end of the mathematical formatting.

So for example $y = \frac{2}{x - 3}$ would be entered as:

$\textcolor{w h i t e}{\text{ddddddd.}}$hash y$\textcolor{w h i t e}{\text{d}}$=$\textcolor{w h i t e}{\text{d}}$2/(x-3) hash.

Note the need to group the x-3 so that the whole of it is used as the denominator.
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color(white)("d")

Input comes before you can get an output
the letter d (for domain) is alphabetically before the letter r (for range).

So d $\to$ 'domain' is input (all the $x$'s)
So r $\to$ 'range' is output (all the $y$'s)

We are told that $y = 2$. This is fixed so the output (range) is always 2

The range is every $x$ that we are 'permitted' to use. This is all $x$'s but 1.

Mathematically we are not 'allowed' to have 0 as a denominator. This situation is called 'the function is undefined'.

Thus we have $x - 3 \ne 0$

Add 3 to both sides $x \ne 3$

Consequently the input (domain) all $x$'s but excluding $x = 3$
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domain is the set of $x$ such that $x$ is in all the real number apart from 3. Using set notation we have: ( I think!)

domain $\to \left\{x : x \in \mathbb{R} , x \ne 3\right\}$
range $\textcolor{w h i t e}{\text{d}} \to \left\{y : y = 2\right\}$