Question

Which function represents the graph of f(x)=|2x| after it is translated 5 units to the left?

Answer 1

As you need to translate to the left this is an horizontal translation so you have to replace f(x) by f(x-h) and when h is less than 0 the graph shifts left, it mean h is negative. So for this problem g(x)= Ι2(x--5)Ι  then g(x) = Ι2(x+5)Ι

Answer 2

Answer:

The answer is the option B

$g\left(x\right)=\left|2(x+5)\right|$

Step-by-step explanation:

we know that

The function $f\left(x\right)=\left|2x\right|$

has the vertex  at point $(0,0)$

The rule of the translation is

$(x,y)-----> (x-5,y)$

The translation of the point $(0,0)$ is equal to

$(0,0)-----> (0-5,0)$

$(0,0)-----> (-5,0)$

so

The function g(x) has the vertex at point $(-5,0)$

therefore

the function g(x) is equal to

$g\left(x\right)=\left|2(x+5)\right|$