Question

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

a.) g(x)=|2(x−5)|
b.) g(x)=|2(x+5)|
c.) g(x)=|2x+5|
d.) g(x)=|2x−5|

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

The answer is the option B

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

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|`