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il63 [147K]
3 years ago
13

Determine the function which corresponds to the given graph. (3 points) a natural logarithmic function crossing the x axis at ne

gative two and y axis at one.
The asymptote is x = -3.

Mathematics
1 answer:
quester [9]3 years ago
4 0

Answer:

y =log_e(x+3)

Step-by-step explanation:

It is given that the graph corresponds to a natural logarithmic function.

That means, the function y has a natural log (Log with base e) of some terms of x.

It is given that asymptote of given curve is at x= -3. i.e. when we put value

x= -3, the function will have a value y \rightarrow \infty.

We know that natural log of 0 is not defined.

So, we can say the following:

log_e(x+a) is not defined at x= -3

\Rightarrow x+a =0\\\Rightarrow x = -a

i.e. x =-a is the point where y \rightarrow \infty

a = 3

Hence, the function becomes:

y =log_e(x+3)

Also, given that the graph crosses x axis at x = -2

When we put x = -2 in the function:

y =log_e(-2+3)  = log_e(1) = 0

And y axis at 1.

Put x = 0, we should get y = 1

y =log_e(0+3)  = log_e(3) \approx 1

So, the function is: y =log_e(x+3)

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