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Consider the function P(x)=x2, which is a parabola that opens upward, with a vertex at (0,0).

It undergoes four separate transformations as indicated by the graphs that follow.

P(x) represents the preimage and is placed correctly on all images. I(x) represents the image after the transformation.

Match each transformation indicated by I(x) to the correct graph.

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I(x)=P(x)−4
I(x)=P(x+4)
I(x)=P(x)+4
I(x)=P(x−4)

Consider the function Pxx2 which is a parabola that opens upward with a vertex at 00 It undergoes four separate transformations as indicated by the graphs that class=

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MrRoyal

The equations and their graphs are:

  • Graph 4: I(x)=P(x)−4
  • Graph 2: I(x)=P(x+4)
  • Graph 1: I(x)=P(x)+4
  • Graph 3: I(x)=P(x−4)

How to match the equations and their graphs?

The parent function is given as:

P(x) = x^2

As a general rule of function transformation, we have:

  • Vertical translation up: I(x) = P(x) + k
  • Vertical translation down: I(x) = P(x) - k
  • Horizontal translation left: I(x) = P(x + k)
  • Horizontal translation right : I(x) = P(x - k)

Using the above rules and the assumption that k is 4;

We have:

  • Vertical translation up: I(x) = P(x) + 4
  • Vertical translation down: I(x) = P(x) - 4
  • Horizontal translation left: I(x) = P(x + 4)
  • Horizontal translation right : I(x) = P(x - 4)

Hence, the graphs of the equations are:

  • Graph 4: I(x)=P(x)−4
  • Graph 2: I(x)=P(x+4)
  • Graph 1: I(x)=P(x)+4
  • Graph 3: I(x)=P(x−4)

Read more about function transformation at:

https://brainly.com/question/4025726

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