Could you describe this function as "logarithmic"? \(\displaystyle{f{{\left({x}\right)}}}={\frac{{{1}}}{{\sqrt{{{x}}}}}}\) As

ideklaraz7xz

ideklaraz7xz

Answered question

2022-03-26

Could you describe this function as "logarithmic"?
f(x)=1x
As x increases, the value of f(x) decreases, but the decrease tapers off quickly as x gets larger, and if you plot the graph of f(x), the shape looks kind of like an upside-down logarithm. Would it be correct to describe this function as declining logarithmically, as x increases?

Answer & Explanation

sa3b4or9i9

sa3b4or9i9

Beginner2022-03-27Added 14 answers

No.
Logarithmic functions are specifically functions that have the property that shifting the function up or down by a fixed amount is roughly equivalent to scaling it horizontally by some fixed factor. Your function f(x)=x12 is not the same in this regard.
For example, your function has a horizontal asymptote at x = 0. A logarithmic function has no horizontal asymptotes.
The function only "looks similar" because it is concave up for x>0 and has a vertical asymptote at x=0. The similarities stop there.

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