Answer:
What is the graph of h(x)=f(x)+g(x) with an example?
So many possible combinations of types of equations for f(x) and g(x).
If they are both linear. f(x) = 3x + 2. g(x) = 2x - 5. h(x) = f(x) + g(x) = 5x - 3. This is also linear.
f(x) has slope = 3 and y-intercept = 2. g(x) has slope = 2 and y intercept = -5. h(x) has slope = 5 and y-intercept = -3.
The graph of the sum of two linear equations is a straight line with slope equal to the sum of the slopes of the two linear equations and a y-intercept equal to the sum of the y-intercepts of the two linear equations.
If one is linear and the other is quadratic. f(x) = 2x + 3. g(x) = x^2 + 6x - 4. h(x) = f(x) + g(x) = x^2 + 8x - 1. This is quadratic.
f(x) has slope = 3 and y-intercept = 3. g(x) has an axis of symmetry of x = -3, vertex at (-3, -13), y-intercept = -4, x-intercepts = -3 + 13^½ and -3 - 13^½ . h(x) has an axis of symmetry of x = -4, vertex at (-4, -17), y-intercept = -1, x-intercepts = -4 + 17^½ and -4 - 17^½ .
The graph of the sum of a linear equation [y = mx + b] and a quadratic equation [y = Ax^2 + Bx + C] has an axis of symmetry of x = - (B + m) / 2A, vertex at ( - (B + m) / 2A, - (B + m)^2 / 4A + (b + C)), y-intercept = b + C, x-intercepts = (- (B + m) + ( (B + m)^2 - 4A (b + C))^½ ) / 2A and (- (B + m) - ( (B + m)^2 - 4A (b + C))^½ ) / 2A .
