Question

Identify the domain of the exponential function shown in the following graph:

Answer 1

Answer:

All real numbers.

Step-by-step explanation:

First of all, an exponential function can be identified by its graph due to its behaviour: a slow growth after the y-interception, and a faster growth after y-intercept point.

Also, exponential functions have the independent variable (x) as exponent, that's why they are called exponential.

Now, if you think this through, notice that powers cannot be equal to zero or negative, the least power is equal to 1, which is the case of having a null exponent.

$x^{0}=1$

This behaviour indicates a restriction for the image of the exponential function, but not to its domain. That's why its domains is defined as all real numbers.

Using the graph, you can observe that the restriction is towards the range, which is y-variable.

Therefore, the right answer is all real numbers.

Answer 2

All real numbers is the correct answer.