Question

can someone please xplain to me how to graph the sum of two functions by hand?

Answer 1

There are two ways, the one with the least writing would be to add the functions together and then make your table of coordinates. that is:
F(x) = x^3+3x+2 and G(x) = 14x^3+3x^2+9
F(x)+G(x) = 15x^3+3x^2+3x+11 Then use this to plug in for points and graph them like you would any function.

The other option would be to make tables of points for both functions, so make a table for F(x) and one for G(x) and then add the Y values across the same values of X to make a new table of coordinates.

Answer 2

I add the y values. It was just hard for me to see the shape of the graph. It was add f(x) = x^2 and g(x) = 1/x and graph.

Answer 3

f(x) + g(x) = x^2+1/x
X | Y
-5 | 24.8
-4 | 15.75
-3 | 8.666666
-2 | 3.5
-1 | 0
0 | Undefined (Asymptote)
1 | 2
2 | 4.5
3 | 9.333333
4 | 16.25
5 | 25.2

You are going to have an upward opening parabola in quadrant III
and a inverse logrthmic across quadrants III and I