Question

Consider the graph of function g below. A diagonal curve declines from (negative 1, 9) through (0, 6), (2, 0), (3, negative 3), (4, negative 6), and (5, negative 9) on an x y coordinate plane. Determine which sequences of transformations could be applied to the parent function f(x) = x to obtain the graph of g. Reflect over the x-axis, vertically stretch by a factor of 3, and then shift up 6 units. Shift right 6 units, reflect over x-axis, and then vertically stretch by a factor of 3. Shift up 6 units, reflect over the x-axis, and then vertically stretch by a factor of 3. Shift right 2 units, reflect over x-axis, and then vertically stretch by a factor of 3. Reflect over the y-axis, vertically stretch by a factor of 3, and then shift up 6 units. Shift left 2 units, reflect over x-axis, and then vertically stretch by a factor of 3.

Answer 1

The parent function, f(x) = x, might undergo the following series of transformations to produce the graph: Reflect over the y-axis, vertical stretch by a factor of 2, and then shift up 6 units.

What is geometric transformation?

It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.

The converted function, when compared to the original function, will be obtained as y = -2x + 6 if we plot it on the coordinate plane.

The only method by which the provided graph may be converted to the coordinates specified in the problem is;

Reflect over the y-axis, multiply the vertical stretch by two, and then move up six units.

Thus, the parent function, f(x) = x, might undergo the following series of transformations to produce the graph: Reflect over the y-axis, vertical stretch by a factor of 2, and then shift up 6 units.

Learn more about the geometric transformation here:

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