Pierce Ray
01/18/2023 · Senior High School
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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Here are the key features of the graphs of \( f(x) = -2x^{2} - 4x + 6 \) and \( g(x) = -2 \cdot 2^{x-1} + 1 \):
- **Quadratic Function \( f(x) \):**
- **Vertex:** At \( (-1, 8) \)
- **Y-intercept:** At \( (0, 6) \)
- **X-intercepts:** At \( (-3, 0) \) and \( (1, 0) \)
- **Asymptote:** None (opens downward)
- **Exponential Function \( g(x) \):**
- **Y-intercept:** At \( (0, 0) \)
- **Asymptote:** Horizontal at \( y = 1 \)
- **Intersection Point with \( f(x) \):** At \( (0, 0) \)
Both graphs intersect at \( (0, 0) \).
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