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Answered

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The graph of F(x), shown below, resembles the graph of G(x) = x2, but it has
been changed somewhat. Which of the following could be the equation of
F(x)?

The Graph Of Fx Shown Below Resembles The Graph Of Gx X2 But It Has Been Changed Somewhat Which Of The Following Could Be The Equation Of Fx class=

Sagot :

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Answer:F(x)=-x2-3

Step-by-step explanation:We are given a function:

The graph of  is also shown in the given question figure.

It is a parabola with vertex at (0,0).

Sign of  is positive, that is why the parabola opens up.

General equation of parabola is given as:

Here, in G(x), a = 1

Vertex (h,k) is (0,0).

As seen from the question figure,

The graph of F(x) opens down that is why it will have:

Sign of  as negative. i.e.

And vertex is at (0,-3)

Putting the values of a and vertex coordinates,

Hence, the equation of parabola will become:

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The expression for [tex]f(x) = -(x-3)^{2}-2[/tex] represents the red curve.

How to derive rigid transformations between two functions

In this question we know that [tex]g(x) = x^{2}[/tex] and an unknown [tex]f(x)[/tex], whose expression can be derived by using the following rigid transformations:

  1. Reflection around the x-axis.
  2. Translation 3 units in the +x axis.
  3. Translation 2 units in the -y axis.

Then, the expression for [tex]f(x) = -(x-3)^{2}-2[/tex] represents the red curve. [tex]\blacksquare[/tex]

To learn more on functions, we kindly invite to check this verified question: https://brainly.com/question/5245372

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