Question

which of the following describes the graph of \\(y = \sqrt3{8x - 64} - 5\\) compared to the parent cube root function?

stretched by a factor of 2 and translated 64 units right and 5 units down
stretched by a factor of 8 and translated 8 units right and 5 units down
stretched by a factor of 2 and translated 8 units right and 5 units down
stretched by a factor of 8 and translated 64 units right and 5 units down

Explanation:

Factor the radicand

Using the Radical Simplification knowledge point

$$
LATEXBLOCK0
$$

Simplify the radical expression

Using the Radical Simplification knowledge point

$$
LATEXBLOCK1
$$

Analyze the transformations

Using the Cube Root Transformations knowledge point

$$
LATEXBLOCK2
$$

Match with the given options

Comparing the derived transformations with the choices:

• Stretched by a factor of 2, translated 8 units right, and 5 units down.

This matches the third option.

Answer:

• stretched by a factor of 2 and translated 64 units right and 5 units down
• stretched by a factor of 8 and translated 8 units right and 5 units down
• stretched by a factor of 2 and translated 8 units right and 5 units down (Correct answer)
• stretched by a factor of 8 and translated 64 units right and 5 units down