1. Find the point(s) of intersection by graphing. a) \( f(x)=x^{2}, g(x)=x+6 \)

To find the points of intersection by graphing, you first plot the two functions: \( f(x) = x^2 \) (a parabola opening upwards) and \( g(x) = x + 6 \) (a straight line). The intersection occurs where the outputs are equal, so you look for the points where the graph of the parabola and the line cross each other. By sketching, you would find visually where they meet. To be a math detective, you can solve the equations as well: set \( f(x) = g(x) \), which results in \( x^2 = x + 6 \). Rearranging gives \( x^2 - x - 6 = 0 \). Factoring reveals the roots, which are \( x = 3 \) and \( x = -2 \). Plugging these back into either function shows the corresponding \( y \)-values, giving you the intersection points at \( (3, 9) \) and \( (-2, 4) \). Voilà!