Is the function ƒ(x) = x⁸ an exponential function? If so, identify the base. If not, why not?

Question

eviant · Answer

@Zepdrix

eviant · Answer

would the base be 8?

Zepdrix · Answer

An exponential is a function in which the thing in the EXPONENT is allowed to vary/change.

Zepdrix · Answer

So for this problem, the EXPONENT is the 8, yes?
8 is a constant value, it does not change.

eviant · Answer

so x would be the base then?

Zepdrix · Answer

Yes x is the base.
And if you remember back to your definition for an exponential function,
it should say something about how the base must not be 1, and also must be constant.

eviant · Answer

I thought the base couldn't be less than 0?

Zepdrix · Answer

Oh right right :)
All the negative values are very bad.

1 is also a weird number since 1 to any power is just 1.
I think they exclude that value as well.

Zepdrix · Answer

Just to wrap it up and make sure it's clear tho,

$\large\rm 8^x$ is an exponential function with base 8, and exponent changing.
$\large\rm x^8$ is a polynomial function with base changing, and exponent 8.

eviant · Answer

@dude

eviant · Answer

@Shadow

dude · Answer

Looks good

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