Question

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What are the domain and range of the function? f(x)=3/5x^5
Domain: (−∞, 0)∪ (0, ∞) Range: (0, ∞)
Domain: (−∞, 0)∪ (0, ∞) Range: (−∞, 0)
Domain: (−∞, ∞) Range: ​(−∞, 0)​
Domain: ​(−∞, 0)∪ (0, ∞)​ Range: (−∞, 0)∪ (0, ∞)

Answer 1

Last one

Domain: ​(−∞, 0)∪ (0, ∞)​ Range: (−∞, 0)∪ (0, ∞)

Explanation:

f(x) = 3/(5x⁵)

Since x is in the denominator, x can not be 0

Domain: all real values of x except 0

For y = 0, x has to be infinite therefore y can not be 0

Range: all real values except 0

Answer 2

Domain: ​(−∞, 0) ∪ (0, ∞)​; Range: (−∞, 0) ∪ (0, ∞)

Explanation:

See attachment.

We want to find the domain and range of the function
`f(x)=(3)/(5) x^5`.

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.