Answer:
the equation of g(x) is, [tex]g(x) = 2x-11[/tex]
Step-by-step explanation:
The transformation of the function is defined as:
[tex]g(x)=f(x+b)[/tex]
where, b represents the horizontal shift.
if b> 0 then, the function f(x) shifts b units left and if b< 0 ; then the function shifts b units right
As per the statement:
The function f(x)=2x−5 is a linear function.
It is given that:
g(x) represent f(x) after a horizontal translation 3 units to the right.
⇒[tex]g(x) =f(x-3)[/tex]
then
[tex]g(x) = 2(x-3)-5[/tex]
⇒[tex]g(x) = 2x-6-5[/tex]
⇒[tex]g(x) = 2x-11[/tex]
Therefore, the equation of g(x) is, [tex]g(x) = 2x-11[/tex]
