Question

Which option below best describes why the domain of g(x) = 5–x is all real numbers but the range of g is not all real numbers? The domain of g is all real numbers because every real number . However, the range of g is not all real numbers because the

Answer 1

The function is

g(x) = 5^(-x)

This question can be easily solved by using a graphing calculator

and plotting the graph of g(x)

In the image below, we can see that for each value of x , there is a corresponding value for g(x)

This means that the function does not have any discontinuities. Therefore,

The domain of g(x) is all real numbers (x ∈ R)

The range is related to the values that can be achieved by g(x),

Since it is a positive exponential function, all values will be g(x)>0

And the range would be (0,∞)