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

1 Answer
Nov 11, 2017

Answer:

#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#