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The function g(x) = x2 is transformed to obtain function h:

h(x) = g(x) − 5.

Which statement describes how the graph of h is different from the graph of g?

A.
The graph of h is the graph of g horizontally shifted left 5 units.
B.
The graph of h is the graph of g horizontally shifted right 5 units.
C.
The graph of h is the graph of g vertically shifted down 5 units.
D.
The graph of h is the graph of g vertically shifted up 5 unit

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Answer:

C. The graph of h is the graph of g vertically shifted down 5 units.

Step-by-step explanation:

Given:

  • g(x) = [tex]x^{2}[/tex]
  • h(x) = g(x) − 5 = [tex]x^{2}[/tex]  -5

The graph of h is different from the graph of g is that the graph of h is the graph of g vertically shifted down 5 units.

We have the general form of transformation:

h (x) = ag(k(x-d)) + c

Because, from the investigation, we noticed that changing the value of c only, and it will cause the function to translate vertically.

When c < 0 (when c is negative), the function is translated downward |c| units.

In this situation, c = -5 so the function is vertically shifted down 5 units.

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Answer:

The graph of h is the graph of g vertically shifted down 5 units.

Step-by-step explanation:

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