Question

What is the equation for the logarithmic function shown in the graph?

f(x) = log x + 1

f(x) = log (x + 1)

f(x) = log x – 1

f(x) = log (x – 1)
On a coordinate plane, a logarithmic function approaches x = negative 1 in quadrant 3 and increases into quadrant 1 and approaches y = 1. It goes through (0, 0) and (2, 0.5).

Answer 1

f(x) = log(x + 1)

Reason: the vertical asymptote x = −1 means the inside must be x + 1. Plugging in (0,0) gives log(0+1)=0, so there is no vertical shift. Also f(2)=log(3) ≈ 0.477 ≈ 0.5, matching the point (2,0.5).