Question

Which of the following graphs could depict the function f(x)=-m(x-d)^1/5 if m and d were positive?

Answer 1

Answer:

Only the second option is correct.

Step-by-step explanation:

The first option is a square root function. Therefore this cannot be the graph of $f(x)=-m(x-d)^{1/5}$.

For the second option the origin lies on the positive x-axis which is what we expect from the graph of $f(x)=-m(x-d)^{1/5}$, and for the negative value of x, $f(x)$ is positive, which is a property of the expression $(x-d)^{1/5}$. Therefore this could be the graph of $f(x)=-m(x-d)^{1/5}$.

In the third option the origin lies on the negative x-axis, and $f(x)$ is positive for postive values of x, something that we do not expect from the graph of $f(x)=-m(x-d)^{1/5}$, therefore this cannot of the right answer.

For the fourth option negative values of x give positive values for $f(x)$, but this graph has its origin at a negative value of x, therefore this cannot be the graph of $f(x)=-m(x-d)^{1/5}$.

Thus only the second option is correct.