12. Tranformations and Symmetry

Question 1

y = ƒ(x) + k

How does k translate the graph?

Answer 1

Vertically.

up if k > 0; down if k < 0

Question 2

y = ƒ(x – h)

How does h translate the graph?

Answer 2

Horizontally.

right if h > 0; left if h < 0

Question 3

y = aƒ(x)

How does a stretch (shrink) the graph?

Answer 3

Veritcally, by a factor of |a|.

Stretches if |a| > 1.

Shrinks if |a| < 1.

Question 4

y = ƒ(ax)

How does a shrink (stretch) the graph?

Answer 4

Horizontally, by a factor of |1/a|.

Shrinks if |a| > 1.

Stretches if |a| < 1.

Question 5

y = –ƒ(x) reflects y = ƒ(x)…

Answer 5

About the x-axis.

(The reflection is vertical)

Question 6

y = ƒ(–x) reflects y = ƒ(x)…

Answer 6

About the y-axis.

(The reflection is horizontal)

Question 7

What order must horizontal transformations be applied?

Answer 7

1. Reflect
2. Change scale (|a| must be factored out of a translation)
3. Translation

Question 8

Symmetry about the y-axis

(even functions)

Answer 8

ƒ(x) = ƒ(–x) for all x.

Question 9

Symmetry about the x-axis

Answer 9

ƒ(x) = –ƒ(x) for all x.

Question 10

Symmetry about the origin

(odd functions)

Answer 10

ƒ(x) = –ƒ(–x) for all x.