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

1 Answer
Tony B
May 3, 2017

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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

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

Tony B

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