Question

The graph of $f\left(x\right)=-|\log (x-3)|+3$ will be

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

Graph of $y=\log x$ is



Now shift this curve towards right by $3$ units
$\Rightarrow y=\log (x-3)$



Now, graph of $y=|\log (x-3)|$ is



We get $y=-|\log (x-3)|$ by inverting the graph of $y=|\log (x-3)|$ with respect to the $x-$ axis.


For $y=-|\log (x-3)|+3,$ we move the curve upwards by $3$ units.


Hence, we got the final graph.