which of the following graphs could depict the function f(x)=m(x+d)^1/5 if both m and d are positive numbers?

Explanation:

The x+d portion indicates we'll have either a left or right shift of d units. Since d is positive, we shift d units to the left. The value of d would have to be negative to have a right shift of d units.

This means that the junction point or turning point must be in the negative x territory. The parent function y = x^(1/5) has its turning point at the origin. So y = (x+d)^(1/5) will have its turning point at (-d,0) for some positive number d.

The exponent 1/5 is in the form 1/n with n = 5 being odd. The odd number tells us we have something like a cube root where it forms an S shape of sorts. Each branch extends on forever to the left and right. Therefore, the domain is the set of all real numbers. We don't have to worry about negative values because we aren't dealing with square roots, fourth roots, sixth roots, etc.

All of these facts point to graph C being the answer.

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