Question

use a graphing utility and the change-of-base property to graph the function.

(y = \log_{6}(x - 1))

which graph is the correct graph of (y = \log_{6}(x - 1))?

all graphs have the viewing window (-1, 10, 1) by (-4, 4, 1).

Explanation:

Apply change-of-base property

Using the Change of Base Formula knowledge point

$$ y = \log_6(x-1) = \frac{\ln(x-1)}{\ln(6)} $$

Determine domain and asymptote

Using the Logarithmic Graphing knowledge point

$$
LATEXBLOCK0
$$

Identify key points

Using the Logarithmic Graphing knowledge point

$$
LATEXBLOCK1
$$

Match with graph options

Using the Logarithmic Graphing knowledge point

$$
LATEXBLOCK2
$$

Answer:

• (A) Graph with vertical asymptote at \(x = 0\) and \(x\)-intercept at \((1,0)\)
• (B) Graph with vertical asymptote at \(x = 1\) and \(x\)-intercept at \((2,0)\) (Correct answer)
• (C) Graph with vertical asymptote at \(x = -1\) and \(x\)-intercept at \((0,0)\)
• (D) Graph with vertical asymptote at \(x = 2\) and \(x\)-intercept at \((3,0)\)