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|

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

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calculista calculista · Answer 2 · 2018-11-26T20:50:42+01:00

Answer:

The answer is the option B

[tex]g\left(x\right)=\left|2(x+5)\right|[/tex]

Step-by-step explanation:

we know that

The function [tex]f\left(x\right)=\left|2x\right|[/tex]

has the vertex at point [tex](0,0)[/tex]

The rule of the translation is

[tex](x,y)-----> (x-5,y)[/tex]

The translation of the point [tex](0,0)[/tex] is equal to

[tex](0,0)-----> (0-5,0)[/tex]

[tex](0,0)-----> (-5,0)[/tex]

so

The function g(x) has the vertex at point [tex](-5,0)[/tex]

therefore

the function g(x) is equal to

[tex]g\left(x\right)=\left|2(x+5)\right|[/tex]

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|

Respuesta :

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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|