Question

Describe the transformations on the following graph of f (x)  log( x) . State the
placement of the vertical asymptote and x-intercept after the transformation. For
example, vertical shift up 2 or reflected about the x-axis are descriptions

Answer 1

a) g(x) = log(x +5)

Answer 2

This is the same function from an earlier post. The graph of f(x)=logx has a vertical asymptote (VA) of the y-axis or the line x=0. The x+5 in the argument of the log horizontally shifts the VA 5 units the left to the line x=-5. (See the attachment that i attached to the earlier post.) You may only take the log of a positive number, and so the domain of y=log x is x>0. If you were substituting numbers into y=log(x+5) you may only sub in x-values that make x+5 positive, thus x+5>0, or x>-5 which is the domain of your function. This is what caused the horizontal shift of the 5 units left.

Answer 3

Thank you