Moderate -0.8 This is a straightforward application of horizontal translation to a standard logarithmic function. Students need only recall that f(x-4) shifts the graph 4 units right, find the x-intercept by solving ln(x-4)=0, and identify the vertical asymptote. It requires basic knowledge of function transformations and properties of ln(x), but involves no problem-solving or novel insight—purely routine application of well-practiced techniques.
2. Given that
$$f ( x ) = \ln x , x > 0$$
Sketch on separate axes the graphs of
i) \(y = f ( x )\)
ii) \(\quad y = f ( x - 4 )\)
Show on each diagram, the point where the graph meets or crosses the \(x\)-axis. In each case, state the equation of the asymptote.
2. Given that
$$f ( x ) = \ln x , x > 0$$
Sketch on separate axes the graphs of\\
i) $y = f ( x )$\\
ii) $\quad y = f ( x - 4 )$
Show on each diagram, the point where the graph meets or crosses the $x$-axis. In each case, state the equation of the asymptote.\\
\hfill \mbox{\textit{SPS SPS FM 2022 Q2 [3]}}