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\( f(x)=x^{2} \) \( g(x)=x^{2}-8 \) We can think of \( g \) as a translated (shifted) version of \( f \). Complete the description of the transformation. Use nonnegative numbers. To get the function \( g \), shift \( f \) up/down/left/right \( \checkmark \) by units.

Ask by Harmon Carroll. in the United States
Feb 22,2025

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Answer

To get the function \( g(x) \), shift \( f(x) \) downward by 8 units.

Solution

The function g(x) = x² - 8 is obtained by shifting f(x) = x² downward by 8 units.

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Bonus Knowledge

To get the function \( g \), shift \( f \) down by 8 units. This means you are taking the original quadratic function \( f(x) = x^2 \) and lowering its entire graph by 8 units on the y-axis, resulting in the new function \( g(x) = x^2 - 8 \). This shifting transformation keeps the shape of the parabola intact but merely moves it vertically, allowing you to easily visualize how the same mathematical concept can have varying outputs based on simple adjustments to its position on the graph.

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