Lesson Miscellaneous problems on plots of functions

Miscellaneous problems on plots of functions

Problem 1

To reflect the plot  f(x) =   over the x-axis  means  to change the sign of the function.


So  ,  reflected over x-axis is  .


Next, the function  ,  stretched horizontally by a factor of 6 is   .

So, the function  g(x) =   is your     ANSWER.

Problem 2

The plot of  y = -6f(x) + 6  is obtained from the parent plot  y = f(x)  by stretching y-axis 6 times, then reflecting about x-axis 

and then shifting 6 units up.



    THEREFORE, since the point (5,-5) was originally on the parent plot y = f(x), 

    we  FIRST  move this point to the new position  (5,-30),

    THEN  reflect this point (5,-30) about x-axis, getting the point (5,30),

    and  AFTER THAT  we move this point (5,30) six units up, getting finally the point (5,36).



This procedure does not depend on what the function f(x) is concretely:  it works for ANY function f(x).