How do you do this?

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A. Domain: all real numbers; Range: all real numbers

B. Domain: all real numbers; Range: y>2

C. Domain: all real numbers; Range: y>0

D. Domain:x<1; Range: y>2

E. Domain: x<1; Range: all real numbers

1 Answer
May 4, 2018

Answer is option #B# i.e. Domain: all real numbers; Range: #y>2#

Explanation:

As #f(x)=5(4)^x+2#

#x# can take any value from #-oo# and #oo# and hence domain is all real numbers.

As #x->-oo#, #f(x)=5(4)^(-oo)+2=5/4^oo+2=0+2#, hence #f(x)->2# and hence minimum value of #f(x)# is #2#

and when #x->oo# #f(x)->oo#

Hence range is #y>2#

and answer is option #B# i.e. Domain: all real numbers; Range: #y>2#