CPM Homework Help : PC3 Problem 8-64

The graphs of $y=f(x)$ and $y=g(x)$ are shown below. Write an equation in terms of $f(x)$ that will transform the graph of $y = f(x)$ into $y = g(x)$ .

Continuous Piecewise graph, labeled f of x, left piece, downward parabola, vertex at the point (negative 1, comma 3), passing between negative 3 & negative 2 on the, x axis, stopping at the point (1, comma negative 1), & ray, starting at (1, comma negative 1), passing through the point (3, comma 3), continuing up & right. Continuous Piecewise graph, labeled g of x, left piece, upward parabola, vertex at the point (2, comma negative 2), passing through the point (0, comma 2), stopping at the point (3, comma 1), & ray, starting at (3, comma 1), passing through the point (6, comma negative 2), continuing down & right.

Step 1:

$g(x)$ is a vertical reflection of $f(x)$ .

Step 2:

The function is then shifted to the right $3$ units.

Step 3:

The function is then shifted up $1$ unit.