what are the domain and range of this exponential function?
what are the domain and range of this exponential function?
Answer
Explanation:
Step1: Recall domain definition
The domain of a function is the set of all possible input - values (x - values). For an exponential function, there are no restrictions on the x - values. The graph extends infinitely to the left and right. So, the domain is all real numbers, which can be written as $(-\infty,\infty)$.
Step2: Recall range definition
The range of a function is the set of all possible output - values (y - values). Looking at the graph, the function approaches the horizontal asymptote $y = - 6$ from above but never reaches it, and it extends upwards to infinity. So the range is $y>-6$, or in interval notation, $(-6,\infty)$.
Answer:
Domain: $(-\infty,\infty)$; Range: $(-6,\infty)$