Question

which transformations have been performed on the graph of $f(x) = \sqrt3{x}$ to obtain the graph of $g(x) = 2\sqrt3{x - 3} + 4$? select each correct answer.(3 correct) - compress the graph closer to the x - axis - translate the graph up - translate the graph to the left - reflect the graph over the x - axis - translate the graph to the right - translate the graph down - stretch the graph away from the x - axis

Explanation:

Step1: Identify vertical stretch factor

For $g(x)=a\sqrt[3]{x-h}+k$, $a=2>1$ means vertical stretch.

Step2: Identify horizontal translation

$h=3$, so shift right 3 units.

Step3: Identify vertical translation

$k=4$, so shift up 4 units.

Answer:

• translate the graph up
• translate the graph to the right
• stretch the graph away from the x-axis