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)`.stretching and compressing functions

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)`.

reflection of functionsFor 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)`.stretching and reflecting functions

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).
  2. Reflect result of first step about x-axis (see Task 2).

On the figure to the right you can see graphs of the functions `y=x^4` and `y=-3x^4`.