Question

consider the linear function f(x) = 2x-4.if the line was translated 3 units up,what would the new equation be?

Answer 1

`f(x)=2x-1`

Explanation:

If we have a linear function of the form
`f(x)=ax-b`,

• Vertical translation of c units up means:

f(x) = ax - b + c

• Vertical translation of d units down means:

f(x) = ax - b - d

• Horizontal translation of c units right means:

f(x) = a(x-c) - b

• Horizontal translation of d units left means:

f(x) = a(x+d) - b

These are the horizontal/vertical translation rules. For the function shown, we apply the first rule and it becomes:

`f(x)=2x-4\\f(x)=2x-4+3\\f(x)=2x-1`

This would be the new equation of the translated function.