Question

The graph shown below expresses a radical function that can be written in the form

f(x)=a(x+k)^1/n+c

What does the graph tell you about the value of n in this function?

Answer Choices:

A) n is a positive even integer
B) n is a positive odd integer
C) n is a negative odd integer
D) n is a negative even integer

Answer 1

Option A

n is a positive even integer

Explanation:

The easisest way to solve this problem is to graph the equation

f(x)=a(x+k)^1/n+c

With arbritary values of a,k, n, c that fit each answer option

Please see attached picture

Suppose,

a = -1,

k = -5 , and

c = 2

Case A.

n is a positive even integer

Say n = 2

f(x)= -(x-5)^1/2 + 2

Correct answer

Case B.

n is a positive odd integer

Say n = 3

f(x)= -(x-5)^1/3 + 2

Not the correct answer

Case C.

n is a negative odd integer

Say n = -3

f(x)= -(x-5)^-1/3 + 2

Not the correct answer

Case D.

n is a negative even integer

Say n = -2

f(x)= -(x-5)^-1/2 + 2

Not the correct answer