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2 years ago

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]2 years 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)

Additional comment

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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