Question 270116: State the equation of the line asymptotic to the graph (if any)
y=(1/4)^x-3. Could you help me with this please? Answer by jsmallt9(3758) (Show Source):
You can put this solution on YOUR website! It is not possible to know whether your equation is
or
Please use parentheses generously to make your problem clear. The first equation should be typed in as
y = (1/4)^(x-3)
I will answer the question for both equations. The key to both solutions is to understand what values a positive number raised to a power can be. Your equations both have a positive number, 1/4, raised to some power. No matter what exponent you put on 1/4, the result will NEVER be:
Zero. (Remember not zero!)
Negative. (Remember 1/4 to a negative power is not a negative number. Negative exponents just mean reciprocals. And any reciprocal of 1/4 is still positive.)
While 1/4 to some power can never be zero, it can, however, be an extremely small positive fraction (i.e. a very tiny fraction just above zero). 1/4 to very large positive powers will be very small fractions near zero. The larger the exponent, the closer we get to zero. This is how an asymptote works.
So for
where y equals a power of 1/4, y = 0 is a horizontal asymptote.
and for
where y equals a power of 1/4 minus 3, then y = 0-3 = -3 is a horizontal asymptote.
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