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The graph of g(x) obtained from the horizontal shrink, reflection and translation of f(x) by a factor of 16, across the x–axis and 2 units downwards is given by the function;
- g(x) = -(16•x)² - 2
Please see the attached graph of g(x)
<h3>What is a transformation of a function?</h3>The transformation of the graph of a function is the shrinking, stretching, reflecting or translating of the graph of the function
The given function is f(x) = x²
- The formula for reflecting a function f(x) across the x–axis to get g(x) is: g(x) = -f(x)
- The formula for shrinking of a function f(x) horizontally by a factor of 16 is g(x) = f(16•x)
- To translate the function, f(x), 2 units down gives; g(x) = f(x) - 2
The graph of g(x), which is a horizontal shrink by a factor of 16, a reflection across the x–axis and a vertical shift of 2 units downwards, is obtained from the function, g(x) = -f(16•x) - 2 = -(16•x)² - 2
Therefore;
- g(x) = -(16•x)² - 2
Please find attached the graph of g(x) created with Sheets
Learn more about the transformation of a function here:
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