Transforming functions

Question 1

Describe the transformation:

i) f(x) + a
ii) f(x) - a

Answer 1

i) f(x) moves up by a units
ii) f(x) moves down by a untis

Question 2

Describe the transformation:

i) f(x + a)
ii) f(x - a)

Answer 2

i) f(x) moves LEFT by a units.
ii) f(x) moves RIGHT by a units.

_{- and + move opposite here}

Question 3

Describe the transformation:
-f(x)

Answer 3

f(x) is reflected in the x-axis (upside down).

Question 4

Describe the transformation:
f(-x)

Answer 4

f(x) is reflected in the y-axis.

Question 5

Describe the transformation:

i) cf(x), where c > 1
ii) cf(x), where 0

Answer 5

Multiply y-values by c.

i) Graph shrinks toward y-axis (y becomes large faster).
ii) Graph stretches away from y-axis (y does not grow as fast).

Question 6

Describe the transformation:
i) f(cx), where c > 1

ii) f(cx), where 0 < c < 1

Answer 6

Divide x-values by c.

i) Graph shrinks toward y-axis .
ii) Graph stretches away from y-axis.

Question 7

Describe all of the function transformations that can be performed on the argument and on the function.

Answer 7