Transformed functions

Question

Write the transformed function in terms of the original function f(x):

 

a. Reflect the graph of f(x) across the y-axis, then stretch vertically by a factor of 5.

 

Answer 1

Let g(x) be the transformed version of f(x).  The general transformations are:

 

      g(x) = a·f(b(x-c)) + d

• a = vertical stretch.  If a<0, it flips f(x) across the x-axis
• b = horizontal stretch.  If b<0, it flips f(x) across the y-axis
• c = horizontal shift - shifts f(x) left or right
• d = vertical shift - shifts f(x) up or down

 

You want a vertical stretch of 5, so that's a = 5.  You want to flip f(x) across the y-axis without stretching it horizontally, so b = -1.  There are no horizontal or vertical shifts, so c and d are 0.

 

     g(x) = 5·f(-x)