Question

The function f(x)=2x−5 is a linear function. Let g(x) represent f(x) after a horizontal translation 3 units to the right.

What is the equation for g(x)?

Answer 1

g(x)=2x-11

Explanation:

Answer 2

the equation of g(x) is,
`g(x) = 2x-11`

Step-by-step explanation:

The transformation of the function is defined as:

`g(x)=f(x+b)`

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.

⇒
`g(x) =f(x-3)`

then

`g(x) = 2(x-3)-5`

⇒
`g(x) = 2x-6-5`

⇒
`g(x) = 2x-11`

Therefore, the equation of g(x) is,
`g(x) = 2x-11`