what is the equation for the logarithmic function shown in the graph?\n$f(x)=\\log x + 1$\n$f(x)=\\log(x +…

Explanation:

Step1: Recall the properties of the parent function (y = \log x)

The parent function (y=\log x) has a vertical asymptote at (x = 0) and passes through the point ((1,0)).

Step2: Analyze the transformation of the given graph

The graph of the function in the picture has a vertical asymptote at (x=- 1). For a logarithmic function (y=\log(x - h)+k), the vertical asymptote is (x = h). Here (h=-1). Also, when (x = 0), (y=\log(0 + 1)=\log(1)=0). For the function (y=\log(x+1)), the vertical asymptote is (x=-1) (using the formula (x - h=0) where (h=-1) for (y = \log(x - h))) and when (x = 0), (y=\log(0 + 1)=0)

Answer:

(f(x)=\log(x + 1)) (the second option)