Question

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

Explanation:

Step1: Identify reflection transformation

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

Step2: Identify vertical stretch transformation

The coefficient $3$ (greater than 1) multiplying $\sqrt{x}$ stretches the graph away from the x-axis.

Step3: Identify vertical translation transformation

The $+4$ at the end of $g(x)$ translates the graph upward by 4 units.

Answer:

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