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The graph of function [tex]g(x)[/tex] is a transformation of the graph of function [tex]f(x)=x^2[/tex].

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



Answer :

To determine the correct transformation applied to the function [tex]\(f(x) = x^2\)[/tex] to obtain the function [tex]\(g(x)\)[/tex], we need to analyze the changes step-by-step.

1. The original function is [tex]\(f(x) = x^2\)[/tex].

2. The given form of the transformed function is [tex]\(g(x) = \boxed{} -2x^2 - 3\)[/tex].

Now let's examine the changes:

- Multiplication by -2:
[tex]\( -2x^2 \)[/tex] reflects the graph of [tex]\(x^2\)[/tex] over the x-axis and stretches it vertically by a factor of 2. The negative sign indicates the reflection, while the 2 indicates the stretch.

- Subtraction of 3:
[tex]\(-3\)[/tex] translates the graph downward by 3 units. This moves every point on the graph down by 3 units.

Combining these transformations, the function [tex]\(g(x)\)[/tex] can be written as:
[tex]\[ g(x) = -2x^2 - 3 \][/tex]

Thus, the correct transformation applied to [tex]\(f(x) = x^2\)[/tex] to get [tex]\(g(x)\)[/tex] is:
[tex]\[ \boxed{} = -2 \][/tex]
\x^2 - 3\)