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 c in this function?

Answer 1

C. c is less than zero

Explanation:

The parent radical function y=x^(1/n) has its point of inflection at the origin. The graph shows that point of inflection has been translated left and down.

Function transformation

The transformation of the parent function y=x^(1/n) into the function ...

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

represents the following transformations:

• vertical scaling by a factor of 'a'
• left shift by k units
• up shift by c units

Application

The location of the inflection point at (-3, -4) indicates it has been shifted left 3 units, and down 4 units. In the transformed function equation, this means ...

• k = 3
• c = -4

The graph says the value of c is less than zero.

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Additional comment

Apparently, the value of 'a' is 2, and the value of n is 3. The equation of the graph seems to be ...

f(x) = 2(x +3)^(1/3) -4