Question

find the interval on which the function is continuous.

y= √ 7x+2

Answer 1

With a square root totally by itself, the only thing that could make an interval not continuous is the square root being less than zero. Because of that, all you need to do is find out on which interval the inside of it will be greater than or equal to zero; you can't have a negative square root, at least without complex numbers getting involved, so you can find out whatever x needs to be to be zero, first.

\[0 = \sqrt{7x + 2} \]\[0 = 7x+2\]\[-2 = 7x\]\[x = -\frac{ 2 }{ 7 }\]
So, the interval should be continuous from x = -7/2 to x = infinity.

Answer 2

Awesome! Thank you so much :D

Answer 3

No problem! Glad it makes sense.