Graphs and transformations

Question 1

y=f(x-a)

Answer 1

Move a to the right

Question 2

y=f(x+a)

Answer 2

Move a to the left

Question 3

y=f(x)-a

Answer 3

Move a down

Question 4

y=f(x)+a

Answer 4

Move a up

Question 5

y=af(x)

Answer 5

Stretch parallel to y axis
x values unchanged
y values multiplied by a

Question 6

y=f(ax)

Answer 6

Stretch parallel to x axis
x values divided by a
y values unchanged

Question 7

y=f(-x)

Answer 7

Reflected in x=0 (y axis)

Question 8

y=-f(x)

Answer 8

Reflected in y=0 (x axis)

Question 9

y= (x+2)^2-2

Min point?

Answer 9

(-2,-2)
Minus the number in bracket (x coordinate)
Number outside bracket (y coordinate)

Question 10

Shape of cubic graph if coefficient of x^3 is positive

Answer 10

Upward then downward sloping

Question 11

y=(x-3)^2 (x+1)

Points it crosses x axis

Answer 11

x=-1

It touches x=3 but does not cross it