Affine Coordinate Changes

The graph of the function f(mx+b) is related to the graph of f(x) in interesting ways.

The graph of the function f(mx+b) is related to the graph of f(x) in interesting ways.

2 Responses to “Affine Coordinate Changes”

  1. Raza on September 3rd, 2021 @ 12:29 pm

    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.

  2. hrm on September 23rd, 2021 @ 10:53 pm

    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.

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