which statement is true?\no the graph of $y = \\log_b(x - 4)$ is the graph of $y = \\log_b(x)$ translated 4…

Explanation:

Step1: Recall translation rules

For a function $y = f(x)$, $y=f(x - h)$ is a horizontal translation. If $h>0$, it shifts right by $h$ units; if $h < 0$, it shifts left by $|h|$ units. And $y=f(x)+k$ is a vertical translation. If $k>0$, it shifts up by $k$ units; if $k < 0$, it shifts down by $|k|$ units.

Step2: Analyze each option

• For $y=\log_b(x - 4)$, compared to $y = \log_b(x)$, it is translated 4 units right (not down).
• For $y=\log_b(x)-4$, compared to $y=\log_b(x)$, it is translated 4 units down (not left).
• For $y=\log_b(x)+4$, compared to $y=\log_b(x)$, since we have $y=f(x)+4$ where $f(x)=\log_b(x)$ and $k = 4>0$, it is translated 4 units up.
• For $y=\log_b(x + 4)$, compared to $y=\log_b(x)$, it is translated 4 units left (not right).

Answer:

The graph of $y=\log_b(x)+4$ is the graph of $y=\log_b(x)$ translated 4 units up.