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

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 .

For the second option the origin lies on the positive x-axis which is what we expect from the graph of , and for the negative value of x, is positive, which is a property of the expression . Therefore this could be the graph of .

In the third option the origin lies on the negative x-axis, and is positive for postive values of x, something that we do not expect from the graph of , therefore this cannot of the right answer.

For the fourth option negative values of x give positive values for , but this graph has its origin at a negative value of x, therefore this cannot be the graph of .

Thus only the second option is correct.

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for