Which quadrants and axes does #f(x)=5sqrt(x+5)# pass through?

1 Answer
Nov 25, 2015

This is a domain and range question.

Explanation:

A radical function can only have a non-negative argument and a non-negative outcome.
So #x+5>=0->x>=-5# and also #y>=0#
This means that #f(x)# can only be in the first and second quadrant.

Since the function is positive when #x=0# it will cross the #y#-axis.
Since #f(x)=0# when #x=-5# it will touch (but not cross) the #x#-axis
graph{5*sqrt(x+5) [-58.5, 58.5, -29.26, 29.3]}