Explain why adding a constant value c to any function does

Question

Question: (a) Graph

f(x) = (1/2)x²

and g(x) = f(x)+3 on the same set of axes. What can you say about the slopes of the tangent lines to the two graphs at the point x = 0? x = 2? Any point x = x0?

(b) Explain why adding a constant value, C, to any function does not change the value of the slope of its graph at any point. [Hint: Let g(x) = f(x) + C, and calculate the difference quotients for f and g.]