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Inga [223]
2 years ago
15

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 te

ll you about the value of c in this function?

Mathematics
1 answer:
MAXImum [283]2 years ago
8 0

Answer:

  C.  <em>c</em> is less than zero

Step-by-step 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.

<h3>Function transformation</h3>

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

<h3>Application</h3>

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.

__

<em>Additional comment</em>

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

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\left[\begin{array}{ccc}2&6&3\\-5&1&4\end{array}\right]

R1 ÷ 2  = \left[\begin{array}{ccc}1&3&1.5\\-5&1&4\end{array}\right]

R2 ÷ -5 = \left[\begin{array}{ccc}1&3&1.5\\1&-0.2&-0.8\end{array}\right]

R2: R1 - R2  = \left[\begin{array}{ccc}1&3&1.5\\0&3.2&2.3\end{array}\right]

R2 ÷ 3.2 =  \left[\begin{array}{ccc}1&3&1.5\\0&1&0.71875\end{array}\right]

R1: R1 - 3R2 = \left[\begin{array}{ccc}1&0&0.65625\\0&1&0.71875\end{array}\right]

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