Question

Given the parent function f(x) = x2 describe the graph of g(x) = (3x-6)2 +3.

Answer 1

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

Answer 2

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

Explanation: