Question

The graph of a linear equation g(x)=-1/3x +2 can be obtained from the graph f(x)=1/3x by using infinite sets of elementary translation (i.e reflection and shifting). List out five of those sets

Answer 1

1. {Rx, T(-6, 4)}
2. {Rx, T(-3, 3)}
3. {Rx, T(0, 2)}
4. {Rx, T(3, 1)}
5. {Rx, T(9, -1)}

Explanation:

We assume you are not interested in five infinite sets of translations. Rather, we assume you want to pick 5 translations from the infinite set of possibilities.

The attached graph shows f(x), g(x), and 5 lines (dashed or dotted) that represent possible reflections and shifts of the function f(x).

The function f1 represents a reflection of f(x) about the x-axis, followed by a left-shift of 6 units. To make it match g(x), we need to shift it upward 4 units. Then the set if translations is ...

g(x) = f(x) ... {reflected over the x-axis, shifted left 6, shifted up 4}

Along the same lines, other possibilities are ...

g(x) = f(x) ... {reflected over the x-axis, shifted left 3, shifted up 3}

g(x) = f(x) ... {reflected over the x-axis, shifted left 0, shifted up 2}

g(x) = f(x) ... {reflected over the x-axis, shifted right 3, shifted up 1}

g(x) = f(x) ... {reflected over the x-axis, shifted right 9, shifted down 1}

___

Additional comment

All of the transformations listed above use reflection in the x-axis. Reflection could use the y-axis, as well. Reflection of the basic function f(x) in the y-axis will have the identical effect as reflection in the x-axis. The listed translations would apply unchanged.