Sketch on the same set of axes the graphs of $$ f(x)=-2 x^{2}-4 x+6 $$ and $$ g(x)=-2 \quad 2^{x-1}+1 $$ Clearly indicate all intercepts with the axes, turning point(s) and asymptote(s).

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Rojas Lynch · Accepted Answer

Here are the key points for the graphs of $$ f(x) = -2x^2 - 4x + 6 $$ and $$ g(x) = -2 \cdot 2^{x-1} + 1 $$: - **Function $$ f(x) $$**: - **Y-Intercept**: $$ (0, 6) $$ - **X-Intercepts**: $$ (-3, 0) $$ and $$ (1, 0) $$ - **Turning Point**: $$ (1, 0) $$ - **Function $$ g(x) $$**: - **Y-Intercept**: $$ (0, 0) $$ - **X-Intercept**: $$ (0, 0) $$ - **Horizontal Asymptote**: $$ y = 1 $$ - **No Vertical Asymptotes** When graphed on the same set of axes, $$ f(x) $$ is a downward-opening parabola with intercepts at $$ (0, 6) $$, $$ (-3, 0) $$, and $$ (1, 0) $$, and a turning point at $$ (1, 0) $$. $$ g(x) $$ is an exponential decay curve that approaches the horizontal asymptote $$ y = 1 $$ and passes through the origin $$ (0, 0) $$.

Sketch on the same set of axes the graphs of \( f(x)=-2 x^{2}-4 x+6 \) and \( g(x)=-2 \quad 2^{x-1}+1 \) Clearly indicate all intercepts with the axes, turning point(s) and asymptote(s).

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Sketch on the same set of axes the graphs of \( f(x)=-2 x^{2}-4 x+6 \) and \( g(x)=-2 \quad 2^{x-1}+1 \) Clearly indicate all intercepts with the axes, turning point(s) and asymptote(s).

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