(a)
\The function is .
Horizontal shrink : , shrink the graph of
horizontally by a factor of
.
Therefore, is the graph of
horizontally shrink by a factor of
.
Graph:
\Graph the function .
(1) Draw the coordinate plane.
\(2) Graph the function .
(3) Shrink the graph of horizontally by a factor of
.
(b)
\The function is .
Horizontal stretch : , stretch the graph of
horizontally by a factor of
.
Therefore, is the graph of
stretched horizontally by a factor of
.
Graph :
\Graph of the function .
(1) Draw the coordinate plane.
\(2) Graph the function .
(3) Stretch the graph of horizontally by a factor of
.
(c)
\The function is .
Reflection : , reflect the graph of
about the
axis.
Therefore, is the graph of
reflect about the
axis.
Graph :
\Graph of the function .
(1) Draw the coordinate plane.
\(2) Graph the function .
(3) Reflect the graph of about the
axis.
(d)
\The function is .
Reflection : , reflect the graph of
about the
axis.
Reflection : , reflect the graph of
about the
axis.
Therefore, is the graph of
reflect about the
axis and reflect about the
axis.
Graph :
\Graph of the function .
(1) Draw the coordinate plane.
\(2) Graph the function .
(3) Reflect the graph of about the
axis and then about the
axis.
(a) Graph of the function is
(b) Graph of the function is
(c) Graph of the function is
(d) Graph of the function is
.