How do you write an equation in the form f(x) = kx^n for the direct variation functions given f(2) = 8 and n = 4?

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How do you write an equation in the form f(x) = kx^n for the direct variation functions given f(2) = 8 and n = 4?

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Answer 1 · 2016-06-15T11:13:29

$f (x) = k x^{n}$ $f(x)=kx^n$ is not a direct variation function

Explanation:

If $f (x)$ $f(x)$ were a direct variation function replacing $x$ $x$ with a multiple of $x$ $x$ would result in the value of $f (x)$ $f(x)$ being multiplied by that same multiple.
To be a direct variation $f (a \cdot x) = a \cdot f (x)$ $f(a*x)=a*f(x)$

However,
if the intended question was simply to fin the value of $k$ $k$
given
$XXX f (x) = k x^{n}$ $color(white)("XXX")f(x)=kx^n$
and
$XXX f (2) = 8$ $color(white)("XXX")f(2)=8$ when $n = 4$ $n=4$
then
$XXX f (2) = k \cdot (2^{4}) = k \cdot 16 = 8$ $color(white)("XXX")f(2)=k*(2^4)=k*16=8$
$\Rightarrow k = \frac{1}{2}$ $rArr k=1/2$

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How do you write an equation in the form f(x) = kx^n for the direct variation functions given f(2) = 8 and n = 4?

1 Answer

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