Related Graphs

Qu 1.  The point ( 2 , 12 ) lies on the graph of y = f(x). What is the equivalent point on the graph of y = 3f(x+4)?

General solution:

  • A number inside the bracket attacks the x coordinate.

  • If a number is not inside the brackets it must be attacking the y coordinate.

If a number attacks the x coordinate, remember to Xchange the operation: 

  • an add is replaced by a subtraction or vice versa

  • a multiplication  is replaced by a division or vice versa

If a number attacks the y coordinate, simplY do as it says eg add 3 if it says add 3.                               

 Particular solution to Qu 1:  point (2, 12) on f(x)    ---->     (2 take away 4, 12 divided by 3) on 3f(x+4); ie (-2,4)

Qu 2  The point (8 , 13) on the graph of f(x) changes to ( ? , ? ) on the graph of f( x + 4 ) - 7.

The X coordinate 5 is attacked by a “+4”; we must remember to X-change the sign to a minus  and so subtract 4 from the 5 to get - 1.

The Y coordinate 13 is attacked by a “- 7” ; easY, we do as it saYs and so subtract 7 from the 13 to get 6.

Conclusion: (5,13) of f(x) goes to (-1,6) on f( x + 4 ) - 7.

Hence graph of f(x) moves 4 to the left and 7 down.