which of the following functions have a domain of (-infinity, positive infinity) and a range of (2, positive infinity)?

Check all that appy:
A. f(x)=3^x+2+2
B. f(x)=3^x-2
C. f(x)= 0.25^x+2
D. f(x)= 0.25^x-2

Question

which of the following functions have a domain of (-infinity, positive infinity) and a range of (2, positive infinity)?

Check all that appy:
A. f(x)=3^x+2+2
B. f(x)=3^x-2
C. f(x)= 0.25^x+2
D. f(x)= 0.25^x-2

mathmale · Answer

First of all, Katie, I see that in all four functions, x can have any value from (-) infinity to (+) infinity.  So all we have to focus on is determining which function has the given range (which I would write as [2,$$\infty).$$  (That's 2 to infinity, including the left endpoint, 2.)

mathmale · Answer

A.  This is basic exponential function. Is the minimum value of this function 2?  or not?
B.  Does this function have a minimum value?  If so, what is it?  Does this function have a horizontal asymptote?  If so, what is it?
C. and D.  Both of these are decaying exponential functions because the base, 0.25, is between 0 and 1.
What conclusion(s) can you draw?

anonymous · Answer

i am going to take a guess and say that A. and C. are the correct answers since 2 is positive...am i correct?