Precalculus Section 2.4 Transformations of Functions
Vertical Shifting: Outside
shifts the graph upward
shifts the graph downward
Ex. 1) Use the graph of to sketch the graph of each function and describe the transformation.
a) b)
Horizontal Shifting: Inside
shifts the graph left
shifts the graph right
Ex. 2) Use the graph of to sketch the graph of each function and describe the transformation.
a) b)
Reflecting Graphs: Negative
graph reflects across the x-axis (outside)
graph reflects across the y-axis (inside)
Ex. 3) Sketch the graph of each function and describe the transformation. Start by graphing the parent function.
a) b)
c)
Assignment page 190 #1-4, 11-15 odds, 33-47 odds not 41
Precalculus Section 2.4 Transformations of Functions Day 2
Vertical Stretching and Shrinking of Graphs: Outside
vertical stretch by a factor of c
(fraction) vertical shrink by a factor of c
Note: If there is a negative number in front, the negative gives a reflection and the number gives a shrink or stretch.
Ex. 4) Use the graph of to sketch the graph of each function.
a) b)
Horizontal Stretching and Shrinking: Inside
horizontal shrink by a factor of
horizontal stretch by a factor of
Ex. 4) Use the graph of to sketch the graph of each function.
a) b)
Even and Odd Functions
Let f be a function.
f is even if for all x in the domain of f.
The graph of an even function is symmetric with respect to the y-axis
f is odd if for all x in the domain of f.
The graph of an odd function is symmetric with respect to the origin.
Ex. 5) Determine whether the functions are even, odd, or neither. If the function is either even or odd, use symmetry to graph the function.
a) b)
c)
Assignment page 190 #5, 7, 9, 17, 23-31 odds, and 61-64 all