Answer:
[tex]f(x)=\log(x-3)[/tex]
Step-by-step explanation:
The parent logarithmic function, f(x) = log(x), has a vertical asymptote at x = 0. It begins in quadrant IV, passes through the x-axis at point (1, 0) and continues into quadrant I. The end behaviours are:
- As x → 0⁺, f(x) → -∞.
- As x → +∞, f(x) → +∞.
When the parent logarithmic function is translated horizontally by n units, we add n to x when the translation is to the left, and subtract n from x when the translation is to the right.
The given graphed logarithmic function crosses the x-axis at point (4, 0), which indicates that it is the parent logarithmic function translated 4 units to the right. Therefore, the equation of the graphed function is:
[tex]\Large\boxed{f(x)=\log(x-3)}[/tex]
