find the equation for the horizontal asymptote and describe the transformation of the function

Question

f(x) = 2( x – 3) - 8 , formed by transformin the function g(x) = 2x

Answer 1

First, we will distribute the 2 in the transformed function, f(x)

f(x) = 2( x – 3) - 8

f(x) = 2x – 6 - 8

f(x) = 2x – 14

Compared to g(x) = 2x, f(x) = 2x - 14 has been shifted down 14 units.

Since the function is a linear function with a defined slope, there is no horizontal asymptote.