Use the image to answer the question.

Question

A v-shaped curve f of x and its reflection g of x are graphed on a coordinate plane. The vertex of f of x is left parenthesis 0 comma 2 right parenthesis. The vertex of its reflection g of x is left parenthesis 0 comma negative 2 right parenthesis.

The graph shows the function  f(x)=|x|+2 . Place the appropriate symbols in the equation of  g(x)  so that  g(x)  is a transformation of  f(x)  that follows the rule  rx−axis .

(1 point)
g(x)=
|x|
2

GPT-4o mini · Answer

To find the equation of $ g(x) $ that represents the reflection of $ f(x) $ across the x-axis, we start with the equation of $ f(x) $: $$ f(x) = |x| + 2 $$ When reflecting a function across the x-axis, we negate the entire function. This means that for $ g(x) $, we will change the sign of $ f(x) $: $$ g(x) = -f(x) $$ Now, substituting $ f(x) $ into this equation: $$ g(x) = -(|x| + 2) $$ Distributing the negative sign: $$ g(x) = -|x| - 2 $$ So the final form of the equation for $ g(x) $ is: $$ g(x) = -|x| - 2 $$ Therefore, you can fill in the blanks as follows: $$ g(x) = -|x| - 2 $$

lol · Answer

answers?

GPT-4o mini · Answer

I apologize for the misunderstanding. Based on your provided format, here is how to express $ g(x) $:

Using the equation of $ f(x) $:

\[ g(x) = -(|x| + 2) \]

Separately, this can be written as:

\[ g(x) = -|x| - 2 \]

In your desired format of filling in the symbols, the answer would be:

\[ g(x) = -|x| - 2 \]

So, using your notation:

\[ g(x) = |x| ; \text{(subtract)} ; 2 \]

However, if you want the simplest answer based on your original message syntax, it would be simply:

\[ g(x) = -|x| - 2 \]

Make sure to insert the appropriate negative sign and operations as you've seen above.

lol · Answer

give me the dang answer plz

GPT-4o mini · Answer

I apologize for any confusion. Based on your original equation format, the answer for $ g(x) $, which is the reflection of $ f(x) = |x| + 2 $ across the x-axis, is:

\[ g(x) = -|x| - 2 \]

In the context of your provided input, you would fill it in as:

g(x) = $-$ |x| - 2

If you just need the symbols filled in:

g(x) = |x| - 2

Thank you for your patience!