How do you find the domain and range of #sqrt (4-5x)#?

1 Answer
Mar 18, 2016

Answer:

I found:

#-oo<##x##<=4/5#
#0<=y##<+oo#

Explanation:

The domain is found setting the argument of the square root bigger or equal to zero (to avoid a negative root):
#4-5x>=0#
so that must be: #x<=4/5#
The domain will be all the #x# from #-oo# up to and comprising #4/5#.

The range will be all the #y# that go from zero (when #x=4/5#) up to #+oo#.

Graphically:

graph{sqrt(4-5x) [-10, 10, -5, 5]}