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
Application
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)
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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.
