If you are given a graph of function h (x). How would you draw k (x)= 0.5 [ h (x+1) + h (x-1)]?

Question

They do not give eqauation of this graph, just the picture and some coordinates. Do you have to draw both h (x+1) and h (x-1) and then just half the height?

Answer 1

Here is an example for $h(x) = x^2$:

• Shift the function by $1$ to the left. The result is $h(x+1)$ (the blue line in the link).

• Shift the function by $1$ to the right. The result is $h(x-1)$ (the red line in the link).

• Draw a line in the middle of both functions. The result is $k(x)$ (the yellow line in the link).

Answer 2

Yes, draw the graph in the middle (for any x) of two.