ESTION 1 \( f(x)=x^{2}-1 \) and \( g(x)=3^{x} \) Sketch the graphs of \( f \) and \( g \) on the same set of axes (ADDENDUM A). Clearly show all intercepts and asymptote(s) on the graph.

To sketch the graphs of \( f(x) = x^2 - 1 \) and \( g(x) = 3^x \), let's start with the key features of each function. For \( f(x) \): - The graph is a parabola opening upwards, shifted down by 1. - The vertex is at (0, -1). - The x-intercepts can be found by setting \( f(x) = 0 \): \[ x^2 - 1 = 0 \implies (x - 1)(x + 1) = 0 \implies x = -1, 1. \] - The y-intercept is when \( x = 0 \): \( f(0) = -1 \). - No asymptotes exist for this function. For \( g(x) \): - The graph is an exponential function with a base of 3. - The y-intercept is at (0, 1) since \( g(0) = 3^0 = 1 \). - The graph approaches the x-axis as \( x \) decreases, but never touches it — this is a horizontal asymptote at \( y = 0 \). When sketching both graphs together, make sure to mark the points (1, 0), (-1, 0), (0, -1) for the parabola and (0, 1) for the exponential. Don't forget the horizontal asymptote for \( g(x) \) as you visually present the two functions on the same axes!