The resulting equation is: [tex]h(x) = \sqrt{x - 3} - 5[/tex]
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This question is solved using the translation concept.
- Translating a function f(x) a units to the right is the same as finding f(x - a).
- Translating a function f(x) a units down is the same as finding f(x) - a.
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Original function:
[tex]f(x) = \sqrt{x}[/tex]
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Translated 3 units to the right
This is f(x - 3), so:
[tex]g(x) = f(x - 3) = \sqrt{x - 3}[/tex]
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Translating 5 units down
This is g(x) - 5, so:
[tex]h(x) = g(x) - 5 = \sqrt{x - 3} - 5[/tex]
Which is the resulting equation.
The image at the end of this answer compared the graph of the original function, in red, with the translated, in blue.
A similar question is given at https://brainly.com/question/23630829.
