Question

The graph of f(x), shown below, resembles the graph of G(x)=x2, but it has been changed somewhat. Which of the following could be the equation of f(x)

Answer 1

Answer:

Step-by-step explanation:

Given that

G(x) = x²

F(x) is similar to G(x),

From the graph, it is seen that, F(x) shifted by -2 on the negative x axis. Also, the graph shifted by -2 on the negative y axis.

From the graph also, F(x) is scaled by a factor of -⅓ of G(x)

Then,

F(x) = -3(x-2)² - 2

Then, the correct answer is B

Answer 2

The equation of the transformed function is $f(x) = -3(x - 2)^2 -2$

The equation of the function is given as:

$g(x) = x^2$

First, the function is shifted two units right.

So, we have:

$g'(x) = (x - 2)^2$

Next, the function is stretched by a factor of 3.

So, we have:

$g'(x) = 3(x - 2)^2$

Next, it is reflected across the x-axis.

So, we have:

$g'(x) = -3(x - 2)^2$

Lastly, the function is shifted down by 2 units.

So, we have:

$g'(x) = -3(x - 2)^2 -2$

Rewrite as:

$f(x) = -3(x - 2)^2 -2$

Hence, the equation of the transformed function is $f(x) = -3(x - 2)^2 -2$

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