Question

which functions graph is a horizontal stretch of the graph of (f(x) = \sqrt3{x - 6})?

a. (g(x) = \frac{1}{4}\sqrt3{x - 6})

b. (g(x) = \sqrt3{\frac{1}{4}(x - 6)})

c. (g(x) = 4\sqrt3{x - 6})

d. (g(x) = \sqrt3{4x - 6})

Explanation:

Define horizontal stretch transformation

$$ g(x) = f(b \cdot x) \quad \text{where } 0 < b < 1 $$

Apply transformation to the given function

$$
LATEXBLOCK0
$$

Evaluate given options

$$
LATEXBLOCK1
$$

Answer:

• A. \(g(x) = \frac{1}{4}\sqrt[3]{x - 6}\)
• B. \(g(x) = \sqrt[3]{\frac{1}{4}(x - 6)}\) (Correct answer)
• C. \(g(x) = 4\sqrt[3]{x - 6}\)
• D. \(g(x) = \sqrt[3]{4x - 6}\)