Combining the parabola and hyperbola through the sum function yields a graph that captures features of both, showcasing the interaction between x^2 and 1/x in the specified viewing window.
To sketch the graph of the sum (f + g)(x), where f(x) = x^2 and g(x) = 1/x, we can add their y-coordinates directly from their respective graphs.
For f(x) = x^2, it is a parabola with a minimum at the origin. The vertex is (0, 0), and the graph extends upward as x increases.
For g(x) = 1/x, the graph is a hyperbola with vertical asymptote at x = 0 and horizontal asymptote at y = 0. The graph approaches the x-axis as x approaches both positive and negative infinity.
To find (f + g)(x), we add the y-coordinates of f(x) and g(x) at each x. The sum function will be (f + g)(x) = x^2 + 1/x.
Graphing this sum function on a calculator will show the combined effect of the two functions. It will exhibit characteristics of both the parabola and the hyperbola. The resulting graph will likely have asymptotes and reflect the behavior of the individual functions.