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True or false: When given the function \( f(x)=x^{3} \), the function \( g(x)=-5 f(x) \) will undergo a reflection due to its negative sign. Enter 1 for true or 2 for false. (1 point)

Ask by Davey Li. in the United States
Jan 23,2025

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True! The function \( g(x) = -5 f(x) \) reflects the original function \( f(x) = x^3 \) across the x-axis. This happens because of the negative sign in front of the \( f(x) \). So you would enter 1 for true! Additionally, the multiplication by -5 also stretches the graph vertically, making it five times taller in absolute terms. By reflecting over the x-axis and stretching, the resulting graph will have the same shape as the original but inverted and elongated, giving it a dramatic new appearance.

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