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

To graph the functions \( f(x) = -2x^{2} - 4x + 6 \) and \( g(x) = -2 \cdot 2^{x-1} + 1 \) on the same axes: 1. **Function \( f(x) \)**: - **Intercepts**: - \( y \)-intercept at \( (0, 6) \) - \( x \)-intercepts at \( (-3, 0) \) and \( (1, 0) \) - **Vertex** at \( (-1, 8) \) - **Asymptotes**: None - **Shape**: Downward-opening parabola 2. **Function \( g(x) \)**: - **Intercepts**: - \( (0, 0) \) - **Asymptote**: Horizontal at \( y = 1 \) - **Shape**: Decreasing exponential curve approaching \( y = 1 \) **Graph Description**: - The parabola \( f(x) \) has its vertex at \( (-1, 8) \) and crosses the \( x \)-axis at \( (-3, 0) \) and \( (1, 0) \). - The exponential function \( g(x) \) starts at the origin \( (0, 0) \) and decreases towards the horizontal asymptote \( y = 1 \). **Intersections**: - The functions intersect at \( (0, 0) \) and possibly at another point, which would require numerical methods to find. **Summary**: Both functions are graphed with their respective intercepts, vertex, and asymptote clearly marked on the same set of axes.