SOLUTION: f(x)=3(0.5)^x what is the domain of f(x): what is the range of f(x); find an intercept of f(x);

Question 424902: f(x)=3(0.5)^x
what is the domain of f(x):
what is the range of f(x);
find an intercept of f(x);
Answer by jsmallt9(3759) (Show Source): You can put this solution on YOUR website!
The domain is the set of all possible inputs (x values). In your function the x is an exponent. Exponents can be any number so the domain is the set of all real numbers.

The range is the set of all possible outputs (y values). The outputs to this function will be the product of 3 and some power of 0.5. To find the range we will need to know what values powers of 0.5 could be. Powers of 0.5, in fact powers of any positive number, can be any positive number. Powers of 0.5 (or any positive number) cannot be zero or negative no matter what the exponent is!! So the powers of 0.5 can be any positive number. And the function output, being 3 times a power of 0.5, can also be any positive number (since 3 times a positive will also be positive). So the range for this function is all positive real numbers.

When I first saw "an intercept" I immediately wondered which kind of intercept, x-intercept or y-intercept? Then I realized there can only be one kind of intercept with this function. Since the range is limited to positive numbers, the y value can never be zero. And if there is no zero value for y then there are no x-intercepts (since the y coordinate on the x axis is zero).

So there can only be y-intercepts and, since this is a function, there can only be one y-intercept. The y-intercept is a point on the y-axis where the x-coordinates are zeros. So we find a y-intercept by using a zero for x:

Since any non-zero number to the zero power is a 1, this becomes:
f(0) = 3*1
or just
f(0) = 3
So the y-intercept for this function is (0, 3)
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