Unit 1: General Functions Transformations

Question 1

transformation

Answer 1

To change a function by adding, subtracting, or multiplying numbers to it

Question 2

translation

Answer 2

A vertical or horizontal shift

Question 3

vertical

Answer 3

up or down

Question 4

horizontal

Answer 4

left or right

Question 5

f(x) + c

Answer 5

vertical shift UP

Examples :

f(x) + 2

f(x) + 3

|x| + 4

x² + 9

Question 6

f(x) – c

Answer 6

vertical shift DOWN

Examples :

f(x) – 3

g(x) – 4

|x| – 2

x² – 1

Question 7

f(x + c)

Answer 7

horizontal shift LEFT

Examples :

f(x + 5)

g(x + 1)

|x + 4|

(x + 1)²

Question 8

f(x – c)

Answer 8

horizontal shift RIGHT

Examples :

f(x – 3)

g(x – 5)

|x – 1|

(x – 4)²

Question 9

scaling

Answer 9

to stretch or compress

Question 10

scale factor

Answer 10

a number you multiply to strech or compress something

Question 11

a*f(x) , where a>1

Answer 11

Vertical stretch (closer to the y-axis)

Examples :

3*f(x)

2.5*g(x)

4x

2x²

Question 12

a*f(x) , where 0 < a < 1

Answer 12

Vertical compression (further from the y-axis)

Examples :

1/8*f(x)

2/3*g(x)

3/4x

1/4x²

Question 13

-a*f(x)

Answer 13

a reflection over the x-axis

Examples :

–2*f(x)

–0.5*g(x)

–2x

–x²