Graph transformations

Question 1

f(x) + a

Answer 1

Graph up or down
x coordinates will stay the same but y will be changed by adding whatever a is.
- 2 will move graph down 2
+6 will move graph up 6

Question 2

f(x+a)

Answer 2

Graph will be moved left or right
y coordinate will stay the same but x will be change.
+a will move graph to the left (negatively)
- a will move graph to the right (positively)

Question 3

-f(x)

Answer 3

All y values will be opposite of previously - 3 will go negative 3, 2 will be -2
0 will remain 0
All x values will remain the same

Question 4

f(-x)

Answer 4

All x values will be opposite of previously-3 will be 3, 2 will be -2
0 will remain 0
All y values will remain the same

Question 5

kf(x)

Answer 5

All y values will be multiplied by k, all x values will remain the same, roots will be the same.
If k>1 graph will be stretched vertically
If k<1 graph will be compressed vertically

Question 6

f(kx)

Answer 6

All x values will be DIVIDED by k, all y values will remain the same.
If k>1 graph will be compressed horizontally
If k<1 graph will be stretched horizontally

Question 7

Remember -

Answer 7

Draw graphs with curves

Best way to draw the, is find all transformed points first then redraw