Which function represents the following graph?

Complete options are attached.

Option D: y = (∛x + 3) + 3

Step-by-step explanation:

To solve this, let's plug in some values into each of the options given.

From the graph, we can see that when x = 0, y ≈ 4.45.

Thus,let's plug in 0 for x into each of the options;

A) y = (√x - 3) + 3

Put 0 for x into the equation.

y = (√0 - 3) + 3

y = (√-3) + 3

Thus will give us a complex root. Thus, it is not the correct answer.

B) y = (√x + 3) + 3

Put 0 for x into the equation.

y = (√0 + 3) + 3

y = (√3) + 3

y = 1.732 + 3

y = 4.732

Thus,this function is not the correct answer.

C) y = (∛x - 3) + 3

Put 0 for x into the equation

y = (∛0 - 3) + 3

y = (∛-3) + 3

y = -1 + 3

y = 2

y is not equal to 4.45 and thus the function is not correct

D) y = (∛x + 3) + 3

Put 0 for x into the equation

y = (∛0 + 3) + 3

y = (∛3) + 3

y = 1.44 + 3

y = 4.44

This is approximately equal to the approximate value of 4.45 on the graph. Thus, it's the correct function.

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step-by-step explanation: