2 Responses to “Affine Coordinate Changes”
It's worth stating the impact of the two parameters m, b.
The graph f(mx +b) is stretched parallel to the y-axis by a factor of m and shifted parallel to the x-axis to the left by |b|.
To see why this is true, its easiest to consider the cases when m=1 and when b=0 separately.
When m=1, then f(x'+b) = f(x) when x'=x-b i.e b spaces to the left.
When b = 0 then f(x'm) =f(x) when x' =x/m so if m is less then 1 this is a stretch. Switching the sign of m reflects in the y-axis.
Thank you for spelling this out, Raza! I think a good use of this Mathlet would be to ask students to provide descriptions like this.