Name: Monica
Who is asking: Other
Question:
I have reproduced one of the graphs that you sent us. This is the graph of y = f(x).
First I want to label the coordinates of some points on the graph. Since, for each point on the graph, the x and y coordinates are related by y = f(x), I can put the coordinates of these points in a list.
If now you wish to plot y = f(x) + 2 then, for each x value, use the table above to finf f(x) and then add 2 to get f(x) + 2. For example when x = 4 then f(x) = 0 so f(x) + 2 = 0 + 2 = 2 and x = 3 then f(x) = 2 so f(x) + 2 = 2 + 2 = 0. Thus I get
On the graph below I plotted y = f(x) + 2 in red and also y = f(x) 3 in green. You also asked if f(x) + 2 and f(x + 2) are different. Yes they are. The placement of the parentheses makes a difference. For example with your graph above, when x = 4, f(x) = 0 and hence f(x) + 2 =0 + 2 = 2. But f(x + 2) = f(4 + 2) = f(2) = 2. In the second expression, since 4 + 2 is inside the parentheses you evaluate it first to get 2 and then use the table for y = f(x) to find f(2). Cheers,Penny
