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Describe how to transform the graph of [tex]f(x) = x^2[/tex] to obtain the graph of the related function [tex]g(x)[/tex]. Then draw the graph of [tex]g(x)[/tex].

1. [tex]g(x) = f(x + 1)[/tex]
2. [tex]g(x) = f(x) - 2[/tex]



Answer :

sqdancefan

Answer:

  1. Shift left 1 unit
  2. Shift down 2 units
    see attached for graphs

Step-by-step explanation:

You want a description of the transformation, and a graph, of the transformed functions, where f(x) = x²:

  1. g(x) = f(x +1)
  2. g(x) = f(x) -2

Transformation

Translation of the graph of a function by (h, k) is accomplished by ...

  g(x) = f(x -h) +k

where the translation is h units to the right, and k units up.

1. f(x+1)

This transformation has (h, k) = (-1, 0), meaning the graph is translated 1 unit left.

2. f(x) -2

This transformation has (h, k) = (0, -2), meaning the graph is translated 2 units down.

Graphs

The graphs of these functions are shown in the attachment.

View image sqdancefan

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