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 [tex]f(x)=-m(x-d)^{1/5}[/tex].
For the second option the origin lies on the positive x-axis which is what we expect from the graph of [tex]f(x)=-m(x-d)^{1/5}[/tex], and for the negative value of x, [tex]f(x)[/tex] is positive, which is a property of the expression [tex](x-d)^{1/5}[/tex]. Therefore this could be the graph of [tex]f(x)=-m(x-d)^{1/5}[/tex].
In the third option the origin lies on the negative x-axis, and [tex]f(x)[/tex] is positive for postive values of x, something that we do not expect from the graph of [tex]f(x)=-m(x-d)^{1/5}[/tex], therefore this cannot of the right answer.
For the fourth option negative values of x give positive values for [tex]f(x)[/tex], but this graph has its origin at a negative value of x, therefore this cannot be the graph of [tex]f(x)=-m(x-d)^{1/5}[/tex].
Thus only the second option is correct.
