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).

To help visualize these functions, think of \( f(x) = -2x^2 - 4x + 6 \) as a classic parabola that opens downward. The intercepts can be found by setting \( f(x) = 0 \) to get the x-intercepts and evaluating \( f(0) \) for the y-intercept. The turning point, a vertex of this parabola, can be found using the vertex formula \( x = -\frac{b}{2a} \). Meanwhile, \( g(x) = -2 \cdot 2^{x-1} + 1 \) is an exponential decay that shifts down and right, with a horizontal asymptote at \( y = 1 \). You can find the y-intercept by evaluating \( g(0) \). For \( f(x) \), the x-intercepts are at the solution to the quadratic equation, found by the quadratic formula, and the y-intercept is \( (0, 6) \). The vertex is found at \( x = -1 \), giving you the turning point \( (-1, 8) \). In contrast, for \( g(x) \), the y-intercept is at \( (0, -1) \). Remember, the horizontal asymptote (as \( x \) increases) for \( g(x) \) is \( y = 1 \). When sketching, ensure to mark these key points to show the relationship between the two functions clearly!