Question

g(x) = -\log_2(x - 3)

a) identify the transformations applied to g(x) = \log_2(x).

b) state the domain and range.

c) determine the x-intercept.

d) graph the function:

Explanation:

Identify transformations

$$
LATEXBLOCK0
$$

Determine domain, range, and x-intercept

$$
LATEXBLOCK1
$$

Plot key points for graphing

$$
LATEXBLOCK2
$$

Answer:

a) Transformations:

• Reflection across the \(x\)-axis.
• Horizontal translation right by 3 units.

b) Domain and Range:

• Domain: \((3, \infty)\) or \(\{x \in \mathbb{R} \mid x > 3\}\)
• Range: \((-\infty, \infty)\) or \(\{y \in \mathbb{R}\}\)

c) x-intercept:

• \((4, 0)\)

d) Graph:

• Vertical asymptote at \(x = 3\).
• Passes through points \((4, 0)\), \((5, -1)\), and \((7, -2)\).