What is the domain and range of y=sqrt(5x+2)?

1 Answer
Tom M.
Nov 11, 2017

x>= -2/5, x inRR
y>=0, y in RR

Explanation:

The domain is the values of x for which we can plot a value for y.
We cannot plot a value for y if the area under the square root sign is negative since you cannot take the square root of a negative (and get a real answer.
To give us the domain:

let 5x+2>=0
5x>= -2
x>= -2/5, x inRR

The range is the values of y we get from plotting this function.
We get our lowest value when x=-2/5

Let x=-2/5
y=sqrt(5(-2/5)+2
y=sqrt(-2+2)

y=sqrt0=0
Any x value greater than -2/5 will give a bigger answer, and as x-> oo, y-> oo also.

So the range is y>=0, y in RR

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