Question

Determine the function which corresponds to the given graph. (3 points) a natural logarithmic function crossing the x axis at negative two and y axis at one.
The asymptote is x = -3.

Answer 1

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: $y =log_e(x+3)$