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The graph of g(x) is obtained by reflecting the graph of f(x)=2|x| over the x-axis. Which equation describes g(x)?

1. g(x)=|2x|

3. g(x)=−|x+2|

4. g(x)=|x+2|

5. g(x)=−|2x|

Respuesta :

ThonyBossa

Answer:

[tex]g(x) = -|2x|[/tex]

Step-by-step explanation:

Let's see the graph of the function f(x). According to the graph, we can see the next

Domain : R ( All real numbers)

Range : { x ∈ R : x ≥ 0}

If we reflecting f(x) over x-axis, the resulting function is the inverse of the function f (x), that is

[tex]g(x) = - f(x)[/tex]

[tex]g(x) = - [2|x|][/tex]

[tex]g(x) = -2|x|[/tex], applying absolute value properties

[tex]g(x) = -|2x|[/tex]   (I)

The graph of (I) is the second picture.

Ver imagen ThonyBossa
Ver imagen ThonyBossa

Answer:

5. g(x) = −|2x|

Step-by-step explanation:

Given function,

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

Since, the reflection rule over x-axis is,

[tex](x, y)\rightarrow (x, -y)[/tex]

i.e. when a function f(x) is reflected over x axis, then the resultant function is -f(x),

Hence, if f(x) is reflected over x-axis to g(x),

Then,

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

i.e. OPTION 5 is correct.

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