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The function [tex]g(x)[/tex] is a transformation of the quadratic parent function, [tex]f(x) = x^2[/tex]. What function is [tex]g(x)[/tex]?

A. [tex]g(x) = 3x^2[/tex]

B. [tex]g(x) = -\frac{1}{3} x^2[/tex]

C. [tex]g(x) = \frac{1}{3} x^2[/tex]

D. [tex]g(x) = -3x^2[/tex]


Sagot :

To determine which transformation of the quadratic parent function [tex]\( f(x) = x^2 \)[/tex] results in the function [tex]\( g(x) \)[/tex], we need to analyze the options given:

A. [tex]\( g(x) = 3x^2 \)[/tex]

- This represents a vertical stretch of the quadratic function [tex]\( x^2 \)[/tex] by a factor of 3.

B. [tex]\( g(x) = -\frac{1}{3}x^2 \)[/tex]

- This represents a vertical compression by a factor of [tex]\(\frac{1}{3}\)[/tex] and a reflection in the x-axis.

C. [tex]\( g(x) = \frac{1}{3}x^2 \)[/tex]

- This represents a vertical compression by a factor of 3.

D. [tex]\( g(x) = -3x^2 \)[/tex]

- This represents a vertical stretch by a factor of 3 and a reflection in the x-axis.

Given the options, without any extra information to specify which particular transformation [tex]\( g(x) \)[/tex] is, we cannot determine a single unique answer. Therefore, the function [tex]\( g(x) \)[/tex] remains indeterminate and is represented as:

[tex]\[ \boxed{\text{None of these are specifically determined to be } g(x) \text{ given the lack of further information.}} \][/tex]
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