Question

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:

Simplify the given function

Using the Horizontal Translation and Vertical Translation knowledge points

$$
LATEXBLOCK0
$$

Identify the horizontal translation

Using the Horizontal Translation knowledge point

$$ \text{Since the term inside is } (x - 2)\text{, the graph is translated } 2\text{ units to the right.} $$

Identify the vertical translation

Using the Vertical Translation knowledge point

$$ \text{Since } 5\text{ is added to the function, the graph is translated } 5\text{ units up.} $$

Identify the stretch or compression

$$ \text{The factor of } 3\text{ outside the radical represents a vertical stretch by a factor of } 3. $$

Identify the reflection

$$ \text{There is no negative sign multiplying the radical or the variable } x\text{, so there is no reflection.} $$

Answer:

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