3 Transforming Graphs

Question 0

From y= f(x)

To y= f(a x)

Answer 0

Stretch in x direction factor 1/a

Question 1

From y= f(x)

To y =a f(x)

Answer 1

Stretch in y direction factor a

Question 2

From y= f(x)

To y= f(x) + a

Answer 2

Translation ( 0/a)

Question 3

From y= f(x)

To y= f( x+ a)

Answer 3

Translation (-a /0)

Question 4

Form Y = 2^x

To y = 2^4x

Answer 4

Stretching factor 1/4 in x direction

Question 5

How to make y = x^2 +3x translated by (-2 /0)

Answer 5

X is replaced by (x +2)

(X +2)^2 + 3(x + 2)

X^2 + 7x +10

Question 6

If f(x) = x^3 - x

Then what does f(2x) =

Answer 6

Stretch factor 1/2 in x direction

And (2x)^3 - (2x) = 8x^3 -2x

Question 7

(What do you tra./stre. By and what do you replace what with)
From y= f(x)
To y = f(x) +a

Answer 7

Translation (0/a)

Y replaced by (y-a)

Question 8

(What do you tra./stre. By and what do you replace what with)
From y= f(x)
To y= f(x-a)

Answer 8

Translation (a/0)

X replaced by (x -a)

Question 9

(What do you tra./stre. By and what do you replace what with)
From y= f(x)
To y = f(x + a)

Answer 9

Translation (-a/0)

Replace x with (x+a)

Question 10

(What do you tra./stre. By and what do you replace what with)
From y= f(x)
To Y = kf(x)

Answer 10

Stretch factor K in y direction

Y is replaced by (1/k)y

Question 11

(What do you tra./stre. By and what do you replace what with)
From y= f(x)
To f(1/k)x

Answer 11

Stretch factor 1/k in x direction

X is replaced (1/k)x

Question 12

(What do you tra./stre. By and what do you replace what with)
From y= f(x)
To y=f(kx)

Answer 12

Stretch factor 1/k in x direction

X is replaced by (kx)

Question 13

(What do you tra./stre. By and what do you replace what with)
From y= f(x)
To y= -f(x)

Answer 13

Reflection in x axis

Y is replaced by -y

Question 14

(What do you tra./stre. By and what do you replace what with)
From y= f(x)
To y=f(-x)

Answer 14

Reflection in y axis

X is replaced by -x

Question 15

Y=x^2

Stretch factor 3 in y direction, translation (2/0)

Answer 15

Y =3x^2

Y=3(x-2)^2

Question 16

Y =f(x)stretch factor 1/2 in x direction

Stretch factor 5 in y direction

Answer 16

y =f(2x)

Y = 5f(2x)

Question 17

Y = 3 x 2^-x

To y= 2^x

Answer 17

Reflection in y axis, stretch factor 3 in y direction

Question 18

Y = f(x)

To y= 2f (x+1)

Answer 18

Translation (-1/0)

Stretch in y direction factor 2

Question 19

When does the order in which you carry out transformations matter

Answer 19

Sometimes when both transformations are to the x or both to the y

Question 20

Y =f(x)

To. Y= f(3x-1)

Answer 20

Translation (1/0) THEN stretch factor 1/3 in x direction

Question 21

Y =x^3 to y= (3-x)^3

Answer 21

Translation (-3/0) reflection in y axis