Question

which transformations have been performed on the graph of $f(x)=sqrt3{x}$ to obtain the graph of $g(x)=-2sqrt3{x}-1$? select each correct answer.(3 correct) reflect the graph over the x-axis translate the graph to the right compress the graph closer to the x-axis stretch the graph away from the x-axis translate the graph to the left translate the graph down translate the graph up

Explanation:

Step1: Analyze reflection transformation

The negative sign in front of the cube root ($-2\sqrt[3]{x}$) reflects $f(x)$ over the x-axis.

Step2: Analyze vertical stretch

The coefficient $2$ (greater than 1) stretches the graph away from the x-axis.

Step3: Analyze vertical translation

The subtraction of 1 ($-2\sqrt[3]{x}-1$) translates the graph downward.

Answer:

• reflect the graph over the x-axis
• stretch the graph away from the x-axis
• translate the graph down