Question

Write a rule for g, described by the transformation of the graph. Then identify the vertex.

Let the graph of g be a vertical shrink by a factor of 1/4 and a reflection in the y-axis, followed by a translation of 3 units right

Answer 1

The graph transformation rule for g is
`\(g(x) = -(1)/(4)f(x-3)\)`, indicating a vertical shrink, y-axis reflection, and 3-unit right translation. The vertex shifts by 3 units to the right.

The rule for the graph transformation of g is
`\(g(x) = -(1)/(4)f(x-3)\)`. This expression signifies a vertical shrink by a factor of (1/4), a reflection in the y-axis (indicated by the negative sign), and a translation of 3 units to the right. The original function f(x) undergoes these changes to yield the transformed graph g(x).

The vertex of the transformed graph is affected by the translation, so if the original vertex is (h, k), the new vertex becomes (h + 3, k). This rule encapsulates the combined effects of the specified transformations on the graph of f.