b Again, we want to translate the graph of f to the graph of g. We know that the factor to do so is c−b. However, this time we want to . Let's try it out with the factor of c−b.
g(x)=f(x+h)
g(x)=m(x+c−b)+b
g(x)=mx+mc−mb+b
We see that whatever translating factor we choose will be multiplied by the slope
m. This means that we have to divide our translating factor by
m to compensate.
mc−b
Let's see if it works now.
g(x)=f(x+h)
g(x)=m(x+mc−b)+b
g(x)=mx+mm(c−b))+b
g(x)=mx+c−b+b
g(x)=mx+c
Since we got the right result,
g(x)=f(x+mc−b) is the expression that horizontally translates
f to
g.