Question

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

Answer 1

Here are the options to the questions:

a.) g(x)=|2(x−5)|

b.) g(x)=|2(x+5)|

c.) g(x)=|2x+5|

d.) g(x)=|2x−5|

The answer is b.) g(x)=|2(x+5)|

Explanation:

The function F(x) = |2x| has the vertex at point (0,0)

The rule of translation is (x,y) -------- (x - 5, y)

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

(x,y) -------- (0 - 5,0)

(x,y) -------- (-5,0)

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

So therefore, the function g(x) is equal to g(x)=|2(x+5)|