Question

Which transformations have been performed on the graph of f(x) =
`\sqrt[3]{x}` to obtain the graph g(x) = 1/4
`\sqrt[3]{x+3}` + 6

Select each correct answer.



(A) reflect the graph over the x-axis

(B) compress the graph closer to the x-axis

(C) translate the graph down

(D) translate the graph to the right

(E) translate the graph to the left

(F) translate the graph up

(G) stretch the graph away from the x-axis

Answer 1

The correct answers are B, E and F

Explanation:

We can find the answer B by noticing the 1/4 put in front of the cube root sign. this 1/4 shirks the value of every y value by 1/4, which in turn makes it closer to the x axis.

We can find answer E by looking at the 3 inside of the cube root symbol. When we add a number underneath the cube root sign, it always moves the value to the left that many spaces.

Finally, we can find F by looking at the 6 at the end. Any number added to the end of an equation as a constant moves the graph up by that many spaces.

Answer 2

To identify the transformations applied to the graph of the function f(x) to obtain g(x), one can analyze the form of the function g(x), which is g(x) = 1/4∛(x+3) + 6.

The transformations are as follows:

1) The factor of 1/4 in front of the cube root ∛(x) compresses the graph closer to the x-axis. This transformation corresponds to option (B).

2) The addition of 3 inside of the cube root shifts the graph of the function to the left. This is due to the effect of modifying the input or x-value before it goes through the transformation of the function. Therefore, the graph is translated to the left by 3 units, which corresponds to option (E).

3) The term +6 after the cube root indicates a vertical shift of the graph. Specifically, the +6 causes the graph to translate 6 units up on the y-axis. This corresponds to option (F).

So, the correct transformations that have been performed on the graph f(x) to get g(x) are options (B), (E), and (F).