graph transformations

Question 1

f(x)+c

Answer 1

shift up by c

Domain same
Range
[a+c, b+c]

Question 2

f(x)-c

Answer 2

shift down by c

Domain same
Range
[a-c, b-c]

Question 3

cf(x)

Answer 3

Change by a factor of c
Vertical stretch

Domain same
Range
[ca, cb]

Question 4

-cf(x)

Answer 4

Change by factor of - c
vertical compression

Domain same
Range
[-cb, -ca]

as a<b
multiply by -c, -cb will be smaller than -ca

Question 5

LARS

Answer 5

left add right subtract

Question 6

f(x-c)

Answer 6

horizontal shift c unitrs right
Range same
domain:[a+c,b+c]

Question 7

f(x+c)

Answer 7

horizontal shift c units left
Range same
domain:[a-c,b-c]

Question 8

f(cx)

Answer 8

horizontal shrink by a factor of c
Range same
domain:[(1/c)a, (1/c)b]

Question 9

f(-cx)

Answer 9

horizontal shrink by a factor of c
Range same
domain:[(-1/c)b, (-1/c)a]
as a<b, -a>-b hence switch

Question 10

-f(x)

Answer 10

reflection about x axis

Question 11

f(-x)

Answer 11

reflection about y-axis