Question

y = 2\sqrt3{x} - 4
identify the transformations.
horizontal compression by ½ and down 4
vertical stretch by 2 and down 4
horizontal compression by ½ and right 4
vertical stretch by 2 and up 4

Explanation:

Step1: Recall transformation rules for cube root functions

The parent function is \( y = \sqrt[3]{x} \). For a function of the form \( y = a\sqrt[3]{x}+k \), \( a \) affects vertical stretch/compression (if \( |a|>1 \), it's a vertical stretch by a factor of \( |a| \); if \( 0<|a|<1 \), it's a vertical compression) and \( k \) affects vertical shift (if \( k>0 \), shift up; if \( k<0 \), shift down).

Step2: Analyze the given function \( y = 2\sqrt[3]{x}-4 \)

• The coefficient \( a = 2 \), so since \( |2|>1 \), there is a vertical stretch by a factor of 2.
• The constant term \( k=-4 \), so since \( k < 0 \), there is a vertical shift down by 4 units.

Answer:

B. Vertical stretch by 2 and down 4