Graph transformation rules

Question 1

f(x)+a

Answer 1

vertical translation of ‘a’ units UP

Question 2

f(x)-a

Answer 2

vertical translation of ‘a’ DOWN

Question 3

f(x+a)

Answer 3

horizontal translation of ‘a’ units LEFT

Question 4

f(x-a)

Answer 4

horizontal translation of ‘a’ units RIGHT

Question 5

af(x)

Answer 5

vertical stretch (y-axis points) by scale factor a

Question 6

f(ax)

Answer 6

horizontal stretch (x-axis points) by scale factor 1/a

Question 7

-f(x)

Answer 7

reflection in x-axis

Question 8

f(-x)

Answer 8

reflection in y-axis