Question

Determine the function which corresponds to the given graph. a natural logarithmic function crossing the y axis at zero and going through the point 5, -1. The asymptote is x = -1

Answer 1

Answer:

$\text{Required function is} f(x)=-\log_6(x+1)$

Step-by-step explanation:

We need to find the function using given condition.

Parent function of log is log x

$f(x)=\log x$

A natural logarithmic function crossing the y axis at zero and going through the point 5, -1. The asymptote is x = -1

Asymptote is x=-1

So, graph will shift 1 unit right.

$f(x)=a\log_b(x+1)$

Passing point: (0,0) and (5,-1)

Using these two point we will get a and b

For point (5,-1)

$-1=a\log_b(5+1)$

$-1=a\log_b6$

Log to exponent change property

$b^{-1/a}=6$

We will rearrange the expression

$b^{-1/a}=6^{-1/-1}$

Now we compare both side to get a and b

So, a=-1 and b=6

Final function we get

$f(x)=-\log_6(x+1)$

Thus, Required function is $f(x)=-\log_6(x+1)$