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Amanda [17]
3 years ago
7

How are exponential functions related to logarithmic functions? Model that with an example.

Mathematics
1 answer:
scoundrel [369]3 years ago
3 0
Exponential functions are related to logarithmic functions in that they are inverse functions. Exponential functions move quickly up towards a [y] infinity, bounded by a vertical asymptote (aka limit), whereas logarithmic functions start quick but then taper out towards an [x] infinity, bounded by a horizontal asymptote (aka limit).
If we use the natural logarithm (ln) as an example, the constant "e" is the base of ln, such that:
ln(x) = y, which is really stating that the base (assumed "e" even though not shown), that:
{e}^{y}  = x
if we try to solve for y in this form it's nearly impossible, that's why we stick with ln(x) = y
but to find the inverse of the form:
{e}^{y}  = x
switch the x and y, then solve for y:
{e}^{x}  = y
So the exponential function is the inverse of the logarithmic one, f(x) = ln x
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Answer:

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Step-by-step explanation:

<u>Graph of Functions</u>

We have two functions:

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Since g(x)=f(x)-2 it will be represented as an identical graph as that for f(x), but vertically displaced 2 units down. Let's check it by plugging some points

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We can notice the values of g(x) are always 2 units below f(x), thus the correct answer is

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