which of the following could be an example of a function with a domain (-infinity,infinity) and a range (-infinity,4)? check all that apply
A.) y=(0.25)^x+4
B.) y=-(3)^X-4
C.) y=-(3)^x+4
D.) y=-(0.25)^x-4

Question

which of the following could be an example of a function with a domain (-infinity,infinity) and a range (-infinity,4)? check all that apply
A.) y=(0.25)^x+4
B.) y=-(3)^X-4
C.) y=-(3)^x+4
D.) y=-(0.25)^x-4

mathmate · Answer

All the choices are of the form $y=ab^x+k$
where a is a multiplicative constant, b is the base of the exponent x, and k is the vertical shift.
y=k is the horizontal asymptote.
The following drawing shows the effect of the parameter a.
|dw:1405818103808:dw|
The effect of 0<b<1 is the same as switching the sign of a.
There are many factors to consider (a,b, k). So choose carefully.  You should end up with two choices.