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 · 2018-11-26T14:50:42-05:00

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

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

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|

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Related Questions

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|