CPM Homework Help : PC Problem 7-30

Using the graph of $f\left(x\right)$ at right, sketch the following functions.

$−2f\left(x\right)$
Hint (a):
1. Reflect across the x-axis.
2. Stretch vertically by a factor of 2.
Answer (a):
$f\left(−x\right) + 1$
Hint (b):
1. Reflect across the y-axis.
2. Shift up 1 unit.
Answer (b):
$\frac { 1 } { f ( x ) }$
Hint (c):

Continuous linear piecewise labeled, f of x, coming from lower left, passing through (negative 5, comma negative 3), turning horizontal at (negative 1, comma 1), turning down at (1, comma 1), turning horizontal at (5, comma negative 1).

Added to graph, red linear piecewise, coming from upper left, passing through (negative 5, comma 6), turning horizontal at (negative 1, comma negative 2), turning up at (1, comma negative 2), turning horizontal at (5, comma negative 2).

Added to graph, red linear piecewise, labeled, z, coming horizontal from left on x axis, turning up at (negative 5, comma 0), turning horizontal at (negative 1, comma 1), turning down at (1, comma 1), passing through (3, comma 0).

Added to graph, vertical lines at, x = negative 2, & x = 3, and blue point at (0, comma 1 half).