finding domain and range of exponential functions?

Question

f(x) = 2 - e ^ (x / 2)

isn't domain usually (-oo, oo) ?
how do you find range? do i need to set it up as an inequality where its ">0" ? steps and an explanation would be helpful. thanks for your help.

Answer 1

domain = (-infinity, +infinity)
range = (2, -infinity)

In this case finding the range is easy, since it's well-known that
e^(x/2) has a range of (0, infinity),
so 2-e^(x/2) would have a range of (2, -infinity).

See link below for graph of exponential function y=e^x (similar to y=e^(x/2))

Answer 2

When a domain is not explicitly given, the domain is the values of x for which the function is defined.
You are right that the domain for f(x) is (-∞, ∞)

The range is all the possible values f(x) that you can get from putting the domain values into the function.

Can you get a negative number out of this function? How about zero? (hint: e^0 = 1 not 0) Are all positive numbers valid outputs of this function? figure these out and you will determine the range.

Answer 3

f(x) = 2 - e^(x/2)

0 = 2 - e^(x/2)

-2 = -e^(x/2)
e^(x/2) = 2
(x/2) = ln(2)
x = 2ln(2)

Domain (-∞,∞)
Range y < 2
x-intercept 2ln(2)
y-intercept 1

For a graph, go to www.calculator.com/calcs/GCalc.html

only typein 2 - e^(x/2)