Cook Washington
05/10/2023 · Senior High School

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

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To sketch the graphs of \( f(x) = -2x^2 - 4x + 6 \) and \( g(x) = -2 \cdot 2^{x-1} + 1 \), find the intercepts, turning points, and asymptotes for each function. For \( f(x) \), the y-intercept is \( (0, 6) \), x-intercepts are \( (-3, 0) \) and \( (1, 0) \), turning point is \( (1, 0) \), and it opens downwards. For \( g(x) \), the y-intercept and x-intercept are both \( (0, 0) \), and it has a horizontal asymptote at \( y = 1 \). Sketch the graphs accordingly, labeling all points and features.

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