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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

Respuesta :

carlosego
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:

C. Compressed horizontally by a factor of 1/3, horizontal shift right 2, vertical shift up 3

Step-by-step explanation:

If a function f(x) is transformed and make f(kx),

f(x) is compressed horizontally by the factor 1/k if k > 1

f(x) is stretched horizontally by the factor 1/k if 0 < k < 1

Also, if f(x) is transformed and make f(x+a),

f(x) is shifted right if a < 0

f(x) is shifted left if a > 0,

Now, if f(x) gives f(x) + k after transformation,

f(x) is shifted vertically k unit up if k > 0,

f(x) is shifted vertically k unit down if k < 0,

Here, the parent function,

[tex]f(x) = x^2[/tex]

transformed function,

[tex]g(x)=(3x-6)^2+3=(3(x-2))^2+3[/tex]

Thus, by the above explanation,

f(x) is compressed horizontally by a factor of 1/3, horizontal shift right 2, vertical shift up 3.

Option C is correct.

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