Given the parent function f (x) = x^2 describe the graph of g (x) = (3x-6) ^2+3

a.

expanded vertically by a factor of 3, horizontal shift left 6, vertical shift up 3

c.

compressed horizontally by a factor of 1/3, horizontal shift right 2, vertical shift up 3

b.

expanded horizontally by a factor of 3, horizontal shift left 6, vertical shift up 3

d.

compressed vertically by a factor of 1/3, horizontal shift right 2, vertical shift up 3

For this case we have the following functions transformation:

Vertical expansions:

To graph y = a * f (x)

If a> 1, the graph of y = f (x) is expanded vertically by a factor a.

f1 (x) = (3x) ^ 2

Horizontal translations

Suppose that h> 0

To graph y = f (x-h), move the graph of h units to the right.

f2 (x) = (3x-6) ^ 2

Vertical translations

Suppose that k> 0

To graph y = f (x) + k, move the graph of k units up.

g (x) = (3x-6) ^ 2 + 3

Answer:

expanded horizontally by a factor of 3, horizontal shift rith 6, vertical shift up 3