transformations of graph

Question 1

y=f(x-a)

Answer 1

horizontal shift right by a units (add a units to x co-ordinate)

(x,y)—>(x+a,y)

Question 2

y=f(x+a)

Answer 2

horizontal shift left by a units (minus a units to x co-ordinates)

(x,y)—>(x-a,y)

Question 3

y=f(ax)

Answer 3

horizontal compression by |a|>0 ( divide x co-ordinate by a)

(x,y)—>(x/a,y)

Question 4

y=af(x)

Answer 4

vertical stretch for |a|>0 (multiply y coordinate by a)

(x,y)—>(x,ay)

Question 5

y=-f(x)

Answer 5

reflection over x axis

(x,y)—>(x,-y)

Question 6

y=f(-x)

Answer 6

refelction over y axis

(x,y)—>(x,-y)

Question 7

y=f(x)+a

Answer 7

vertical translation up a units

(x,y)—>(x,y+a)

Question 8

y=f(x)-a

Answer 8

vertical translation down a units

(x,y)—>(x,y-a)

Question 9

if change is inside brackets for f(x)

Answer 9

basically just reverse the change
e.g. if multiplying by a number just then divide by that number, if adding by a number subtract by that number ON X COORDINATES

Question 10

if change is outside brackets (affecting f(x))

Answer 10

then change is happening to y coordinate and be normal