math 2: transformations & symmetry

Question 1

3 types of transformations;

Answer 1

translations, stretches/shrinks, reflectrions

Question 2

y= f(x) + k translates y = f(x)

Answer 2

k units vertically

Question 3

y = f(x-h) translates y = f(x)

Answer 3

h units horizontally

Question 4

y = af(x) stretches/ shrinks f(x)

Answer 4

vertically by a factor of |a|

Question 5

y = f(ax) shrinks/ stretches

Answer 5

f(x) horizontally by a factor of |1/a|

Question 6

y = -f(x) reflects y = f(x)

Answer 6

about the x-axis

Question 7

y = f(-x) reflects y=f(x)

Answer 7

about the y-axis

Question 8

symmetry about the y-axis

Answer 8

f(x) = f(-x) for all x

Question 9

symmetry about the x-asix:

Answer 9

f(x)= -f(x) for all x

Question 10

symmetry about the origin:

Answer 10

f(x) = -f(-x) for all x