Question

Suppose that F(x) = x^2 and G(x) = - 1/3 (x+4)^. Which statement best compares
the graph of G(x) with the graph of F(x)?
O A. The graph of G(x) is the graph of F(x) compressed vertically,
flipped over the x-axis, and shifted 4 units to the left.
B. The graph of G(x) is the graph of F(x) compressed vertically,
flipped over the x-axis, and shifted 4 units to the right.
C. The graph of G(x) is the graph of F(x) stretched vertically, flipped
over the x-axis, and shifted 4 units to the left.
D. The graph of G(x) is the graph of F(x) stretched vertically, flipped
over the x-axis, and shifted 4 units to the right.

Answer 1

The statement that describes the transformations needed to go from F(x) to G(x) is statement A.

Which statement compares the graphs of G(x) and F(x)?

First, we know that:

$F(x) = x^2\\\\G(x) = -(1/3)*(x + 4)^2$

Now, notice that we can rewrite G(x) as:

$G(x) = -(1/3)*F(x + 4)$

So, if we start with F(x) and first we apply a vertical compression of scale factor K = 1/3, we get:

$g(x) = (1/3)*F(x)$

If now we apply a reflection over the x-axis, we get:

$g(x) = -(1/3)*F(x)$

Finally, we need to apply a translation of 4 units to the left, so we get:

$g(x) = -(1/3)*F(x + 4) = G(x).$

Then the correct statement is the one in option A.

"The graph of G(x) is the graph of F(x) compressed vertically, flipped over the x-axis, and shifted 4 units to the left."

If you want to learn more about transformations:

https://brainly.com/question/4289712

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