Is #f(x) =x^4sqrt(5-x)# a function?

Answer 1
Yes, it is. Given any value of #x# we never get two values for #f(x)# (We sometimes get no value, but that has to do with the domain, not with being a function.)

This was posted under "Vertical Line Test" which requires a graph. Using graphing technology, here is the graph:

graph{y=x^4sqrt(5-x) [-27.3, 37.68, -4.73, 27.74]}

It is hard to see the graph, and scrolling out makes it look weird.

Here's a similar graph with the scale changed so that each #1# on the #y#-axis represents 100: (I divided the function by 100.)

graph{y=(x^4sqrt(5-x))/100 [-18.8, 21.77, -2.49, 17.79]}

It is fairly clear that this graph passes the vertical line test.

(It is also fairly clear that the domain is #x <= 5#)
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Answer 2

Yes, the function f(x) = x^4 * sqrt(5 - x) is indeed a function.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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