Answer:
Domain: (−∞, 0) ∪ (0, ∞); Range: (−∞, 0) ∪ (0, ∞)
Step-by-step explanation:
See attachment.
We want to find the domain and range of the function [tex]f(x)=\frac{3}{5} x^5[/tex].
The domain is the set of all possible x-values that are included in the function, while the range is the set of all possible y-values that are included in the function.
Look at the graph.
We can see that the x-values can go into infinity except when approaching the line x = 0. Here, the function will never touch x = 0 because that would make the graph undefined. So, we can say that the domain is all real numbers except for x = 0, or (−∞, 0) ∪ (0, ∞).
It's the same thing with the y-values. Although it looks like the line is touching the y-axis, or the line y = 0, the graph actually is not - it's just going really close to it. So, the range is again (−∞, 0) ∪ (0, ∞).
Thus, the answer is D.
