Questions: What kind of transformation converts the graph of f(x)=-2x-4 into the graph of g(x)= -8x-4 ? horizontal stretch vertical shrink horizontal shrink vertical stretch

Solution Steps

To determine the transformation that converts the graph of \( f(x) = -2|x| - 4 \) into the graph of \( g(x) = -8|x| - 4 \), we need to compare the coefficients of the absolute value terms in both functions. The transformation involves a change in the vertical scaling of the graph. Specifically, the coefficient of \(|x|\) changes from \(-2\) to \(-8\), indicating a vertical stretch by a factor of 4.

To determine the transformation from \( f(x) = -2|x| - 4 \) to \( g(x) = -8|x| - 4 \), we compare the coefficients of \(|x|\) in both functions. The coefficient changes from \(-2\) to \(-8\).

The change in the coefficient from \(-2\) to \(-8\) indicates a vertical transformation. Specifically, the absolute value of the coefficient increases from \(2\) to \(8\), which is a factor of \(\frac{8}{2} = 4\).

Since the absolute value of the coefficient increases, this indicates a vertical stretch. A vertical stretch occurs when the graph is stretched away from the x-axis by a factor greater than 1.

Final Answer