Anonymous

# domain and range of a function?

how do you find domain and range? and how would i find it for f(x)=3^x

Relevance

The numbers that cannot be in the domain are typically ones that give you a zero in the denominator (undefined) or numbers that are negative inside a square root. For example x=1 is not in the domain of 1/(x-1). Also x=0 is not in the domain of sqrt(x-1) since the sqrt(0-1) = sqrt(-1) is not defined for real numbers. The domain for 3^x is (-infinity, infinity) since any x can be plugged in.

The range of y-values is significantly more complicated, so you need to learn some special cases. For an exponential function 3^x, the range is (0,infinity).

• To find the domain and range of f(x) = 3^x, the only way to do this is with your understanding of the function.

For one thing this is an exponential function, and exponential functions have no restriction on what x can be (i.e. you can take 3^x of any real number x). Therefore, the domain is R.

For range, it's worth recognizing that exponential functions always have a horizontal asymptote. Whenever the function

f(x) = a^x + b

is written, the horizontal asymptote is b. Therefore, this is what f(x) CANNOT be. For your function above, there's really a 0 in place of b; it's just not there. For that reason, 0 is what f(x) CANNOT be.

So the range is (-infinity, 0) U (0 to infinity)

• domain is simply every value x could be and range is every value y could be