Transformations of functions (Chapter 2)

Question 1

y=f(x)+c

Answer 1

vertical translation
c>0 up
c<0 down

Question 2

y=f(x+b)

Answer 2

horizontal translation
b>0 left
b<0 right

Question 3

y=kf(x)

Answer 3

vertical dilation
k>1 function stretched
0<k<1 function compressed
k<0 function flipped on x-axis

Question 4

y=f(ax)

Answer 4

horizontal dilation (by scale factor 1/a)
a>1 compressed
0<a<1 stretched
a<1 flipped on y-axis

Question 5

dilations always come ____ translations

Answer 5

before

Question 6

y=kf(a(x+b))+c

Answer 6

• horizontal dilation of scale factor 1/a
• horizontal translation of scale factor b
• vertical dilation of scale factor k
• vertical translation of scale factor c

Question 7

do horizontal transformations affect domain or range?

Answer 7

domain
(x-values)

Question 8

do vertical transformations affect domain or range?

Answer 8

range
(y-values)