Question

use the equation \\(y = \sqrt3{27x - 54} + 5\\)
which is an equivalent equation of the form \\(y = a\sqrt3{x - h} + k\\)?

• \\(y = -27\sqrt3{x + 2} + 5\\)
• \\(y = -3\sqrt3{x + 2} + 5\\)
• \\(y = 3\sqrt3{x - 2} + 5\\)
• \\(y = 27\sqrt3{x - 2} + 5\\)

which of the following describes the graph of \\(y = \sqrt3{27x - 54} + 5\\) compared with the parent cube root function?
horizontal translation:
vertical translation:
stretch/compression:
reflection:

Explanation:

Factor the radicand

Using the Radical Simplification knowledge point

$$
LATEXBLOCK0
$$

Simplify the radical

Using the Radical Simplification knowledge point

$$
LATEXBLOCK1
$$

Identify horizontal translation

Using the Horizontal Translation knowledge point

$$
LATEXBLOCK2
$$

Identify vertical translation

Using the Vertical Translation knowledge point

$$
LATEXBLOCK3
$$

Identify dilation and reflection

Using the Cube Root Transformations knowledge point

$$
LATEXBLOCK4
$$

Answer:

Question 1

• (A) \(y = -27\sqrt[3]{x + 2} + 5\)
• (B) \(y = -3\sqrt[3]{x + 2} + 5\)
• (C) \(y = 3\sqrt[3]{x - 2} + 5\) (Correct answer)
• (D) \(y = 27\sqrt[3]{x - 2} + 5\)

Question 2

• Horizontal translation: Shift right 2 units
• Vertical translation: Shift up 5 units
• Stretch/compression: Vertical stretch by a factor of 3
• Reflection: None