Find the equation of the logarithmic function with the x intercept (-17.5, 0) and the y intercept (0, 17.428) and the vertical asymptote is -17.5?

Answer 1

x asymptote = -17.5

parent function

y = logx

shift left 17.5 to get

y = log(x+17.5)

x intercept then is -17.5+1 = -16.5, when y=0, 0=log(x+17.5) when x+17.5 = 1, -16.5+17.5=1

the x intercept can't be -17.5, if the vertical asymptote is the same number, -17.5

the vertical asymptote would then be x=-17.5 which means x approaches but never reaches -17.5, so x can never be -17.5

if you intended to write x intercept =-16.5, not -17.5 then with y intercept =17.428, the equation becomes

y = log(x+16.5) + 16.211

as

log(0+16.5) = log16.5= 1.2175

17.428 = 1.2174+ 16.211

and the vertical asymptote would be when log(x+17.5) is undefined, at log0 when x=-17.5