CPM Homework Help : INT2 Problem 9-141

Copy the graph of $y = f(x)$ at right onto graph paper, and then graph each of the following transformations.

$y = f(x) - 1$
$y = -f(x)$
$y = f(x - 1)$

Piecewise graph with 3 connected sections First: semicircle, passing through the points (negative 5, comma negative 1), (negative 3, comma 1), & (negative 1, comma negative 1). Second: Segment from the point (negative 1, comma negative 1), to the point (2, comma 2). Third: Ray from the point (2, comma 2), passing through the point (5, comma negative 4).

Hint (a):

This transformation is a translation along the $y$ axis. Piecewise graph with 3 connected sections First: semicircle, passing through the points (negative 5, comma negative 2), (negative 3, comma 0), & (negative 1, comma negative 2). Second: Segment from the point (negative 1, comma negative 2), to the point (2, comma 1). Third: Ray from the point (2, comma 1), passing through the point (5, comma negative 5).

Answer (a):

Hint (b):

A negative coefficient in front of $f(x)$ means the graph needs to be reflected over the $x$ axis. Piecewise graph with 3 connected sections First: semicircle, passing through the points (negative 5, comma 1), (negative 3, comma negative 1), & (negative 1, comma 1). Second: Segment from the point (negative 1, comma 1), to the point (2, comma negative 2). Third: Ray from the point (2, comma negative 2), passing through the point (5, comma 4).

Answer (b):

Hint (c):

This transformation is a translation along the $x$ axis. Piecewise graph with 3 connected sections First: semicircle, passing through the points (negative 4, comma negative 1), (negative 2, comma 1), & (0, comma negative 1). Second: Segment from the point (0, comma negative 1), to the point 3, comma 2). Third: Ray from the point (3, comma 2), passing through the point (6, comma negative 4).

Answer (c):