Question

How do you graph `y=sqrt(x-0.5)`, compare it to the parent graph and what is the domain and range?

Answer 1

See explanation

`x in RR and y in RR larr" what is called Real Numbers"`

Domain `->" input "-> x>=0.5 -> [0.5,+oo)`
Range `->" output "->y-> (-oo, +oo)`

Explanation:

Just for identification purposes:

Identify the standardised graph of `y=x` by the name `G_1`

Identify the graph of `y=x-0.5` by the name `G_2`
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`color(blue)("The affect of subtracting 0.5 from "x)`

Step 1:

Using `G_1` look at the ordered pair point of `(x-0.5,y)`

Step 2:
Now go to `G_2` and plot the y value for `G_1` against the `x` for `G_2`

Effectively it is 'shifting' `y=x` to the right by 0.5
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To plot the root we have to remember that the square root of a value has a `+-` type answer

So we actually have `y=+-sqrt(x-0.5)`

Thus we plot two graphs.`" One for "y=+sqrt(x-0.5)`
`" One for "y=-sqrt(x-0.5)`
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There is a set of numbers given the name 'Complex Numbers'

To avoid entering that 'realm' of mathematics we do not permit `x-0.5<0`