SOLUTION: Graph f(x)=(3^-x)-2 and determine the domain, range and vertical asymptote of f.
Algebra.Com
Question 433498: Graph f(x)=(3^-x)-2 and determine the domain, range and vertical asymptote of f.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Graph f(x)=(3^-x)-2 and determine the domain,
range and vertical asymptote of f.
-------------
f(x) = 3^(-x) - 2
f(x) = (1/3)^x -2
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Domain: All Real Numbers
Explanation: The domain of a function is "all Real
Numbers" unless there is some pattern in its rule
which excludes certain numbers. Examples are:
1. a variable expression in the denominator which
could cause the denominator to be zero;
2. an even-root expression with a variable that
could cause the radicand to be negative;
3. a randical expression in a log or ln term that
could be negative or zero.
If none of these are present in the rule of a function,
the Domain is "All Real Numbers".
====================================================
Range: y>= -2
Explanation: 3^-x = (1/3)^x has a minimum value of zero.
So y will have a minimum value of -2.
---------------------------------------------
Vertical Asympt: none
Explanation: There is no variable expression in a denominator.
====================================================
Horizontal Asympt: y = -2
Explanation: As x approaches infinity, (1/3)^x approaches
zero, so y approaches -2.
================================
Cheers,
Stan H.
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