How do you find the domain and range of #f(t) = 3sqrt(t + 4)#?

1 Answer
Jun 21, 2016

Answer:

Assuming we are restricted to Real values:
Domain: #t in [-4,+oo)#
Range:#f(t) in [0,+oo)#

Explanation:

#3sqrt(t+4)# is only defined (in Real values) if #t+4>=0#
#rArr t>=-4#
however, it is defined for all #t >= -4#;
therefore the Domain is #t >=-4 or t in [-4,+oo)#

#sqrt(t+4) >= 0# (by definition of the square root function)
It is equal to #0# when #t=-4#
As #trarr+oo#
#color(white)("XXX")sqrt(t+4)rarr +oo# (and so does #3sqrt(t+4)#)
Therefore the Range is #f(t) > 0 or f(t) in [0,+oo)#