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GarryVolchara [31]
1 year ago
10

The shape of f(x) = √ x, but shifted nine units to the left and then reflected in both the x-axis and the y-axis

Mathematics
1 answer:
mr_godi [17]1 year ago
6 0

Answer:

  g(x) = -√(-x +9)

Step-by-step explanation:

The relevant transformations are ...

  • f(x -h) . . . . . shifts the graph of f(x) right h units
  • f(x) +k . . . . . shifts the graph of f(x) up k units
  • -f(x) . . . . . . . reflects the graph of f(x) over the x-axis
  • f(-x) . . . . . . . reflects the graph of f(x) over the y-axis

<h3>Application</h3>

Applying the transformations in the specified order, we have ...

  f(x) = √x

  f(x +9) = √(x +9) . . . . . . . shifted 9 units to the left

  -f(x +9) = -√(x +9) . . . . . . shifted 9 left, reflected in the x-axis

  -f(-x +9) = -√(-x +9) . . . . shifted 9 left, reflected in x-axis, reflected in y-axis

The shifted, reflected function is ...

  g(x) =  -√(-x +9)

__

<em>Additional comment</em>

The graph shows the original f(x) = √x function in red. The shifted, reflected function is shown in blue. Note that the initial left shift changes appearance to a right shift when it is reflected over the y-axis.

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