Question

find the corresponding graph of $-\log_{2}(x - 3)$

Explanation:

Step1: Identify parent function

Parent function: $y=\log_2(x)$

Step2: Apply horizontal shift

Shift right by 3 units: $y=\log_2(x-3)$

Step3: Apply vertical reflection

Reflect over x-axis: $y=-\log_2(x-3)$

Step4: Analyze key features

• Vertical asymptote: $x=3$ (from $x-3=0$)
• When $x=4$, $y=-\log_2(4-3)=-\log_2(1)=0$, so the graph passes through $(4,0)$
• As $x\to 3^+$, $y\to +\infty$; as $x\to +\infty$, $y\to -\infty$

Answer:

The corresponding graph is the green (first) graph (the one with vertical asymptote at $x=3$, passing through $(4,0)$, decreasing from $+\infty$ to $-\infty$ as $x$ increases past 3).