Question

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|

Answer 1

5. g(x) = −|2x|

Explanation:

Given function,

`f(x) = 2|x|`

Since, the reflection rule over x-axis is,

`(x, y)\rightarrow (x, -y)`

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.

Answer 2

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

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

`g(x) = - f(x)`

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

`g(x) = -2|x|`, applying absolute value properties

`g(x) = -|2x|` (I)

The graph of (I) is the second picture.