Question

what are the domain and range of the function on the graph? the domain includes all integers, and the range is y ≥ 0. the domain includes all integers, and the range is y > 0. the domain includes all real numbers, and the range is y ≥ 0. the domain includes all real numbers, and the range is y > 0.

Explanation:

Step1: Recall the definition of domain

The domain of a function is the set of all possible input values (x - values). For the given graph (which is an exponential - like function), there is no restriction on the x - values. Any real number can be plugged into the function. Integers are a subset of real numbers. So, the domain includes all real numbers.

Step2: Recall the definition of range

The range of a function is the set of all possible output values (y - values). Looking at the graph, as \(x\to-\infty\), \(y\) approaches \(0\) but never actually reaches \(0\) (since the graph never touches the x - axis), and as \(x\) increases, \(y\) gets larger and larger. So, \(y>0\).

Answer:

The domain includes all real numbers, and the range is \(y > 0\).