# Drawing Graph of the Function y=mf(x)

Task 1. Draw graph of the function y=mf(x), where m>0,m!=1, knowing graph of the function y=f(x). We obtain y-coordinates of points of the graph of the function y=mf(x) by multiplying corresponding y-coordinates of points of the graph of the function y=f(x) by number m. Such transformation of graph of the function y=f(x) is called stretching from x-axis with coeffcient m if m>1, and compressing to x-axis, if 0<m<1.

On the figure to the right you can see graphs of the functions y=log_2(x) and y=0.5 log_2(x).

Task 2. Draw graph of the function y=-f(x), knowing graph of the function y=f(x). For same values of x, y-coordinates of functions y=f(x) and y=-f(x) have same y-ordinates but with opposite signs. Therefore, we can obtain graph of the function y=-f(x) by reflecting graph of the function y=f(x) about x-axis.

On the figure to the left you can see graphs of the functions y=(10)^x and y=-(10)^x.

Task 3. Draw graph of the function y=mf(x), where m<0,m!=-1, knowing graph of the function y=f(x). Since mf(x)=-|m|f(x), then we can obtain graph of the function in two steps:

1. Stretch (compress) graph of the function y=f(x) by coeffcient |m| (see Task 1).
On the figure to the right you can see graphs of the functions y=x^4 and y=-3x^4.