pre-calculus lesson 3: translations of function graphs vertical and horizontal shifts in graphs of...
TRANSCRIPT
Pre-Calculus Lesson 3: Translations of Function GraphsVertical and horizontal shifts in graphs of various functions
The Absolute Value FunctionWhat does the graph of y = |x| look like?
y =|x|
y
x
10
10
-10-10
y =|x|+3
y
x
10
10
-10-10
y =|x|+3
y
x
10
10
-10-10
y =|x|-3
y
x
10
10
-10-10
y =|x|-3
y
x
10
10
-10-10
Observation #1:Adding to or subtracting from a function will shift the graph of the parent function up or down, respectively.
y =|x+3|
y
x
10
10
-10-10
y =|x+3|
y
x
10
10
-10-10
y =|x-3|
y
x
10
10
-10-10
y =|x-3|
y
x
10
10
-10-10
Observation #2:Adding to or subtracting from the variable will shift the graph of the parent function left or right, respectively.
y =-|x|
y
x
10
10
-10-10
y =-|x|
y
x
10
10
-10-10
http://www.uiowa.edu/~examserv/mathmatters/tutorial_quiz/geometry/typesofsymmetry_clip_image017.gif
f(x)f(-x)
Observation #3:Negating the function will reflect the parent function over the x-axis. Negating the variable will reflect the parent function over the y-axis.
Even and Odd Functions An even function
is: Symmetric with
respect to the ______________.
Defined by the equation ______________.
An odd function is: Symmetric with
respect to the ______________.
Defined by the equation ______________.
Even and Odd Functions An even function
is: Symmetric with
respect to the ______________.
Defined by the equation ______________.
An odd function is: Symmetric with
respect to the ______________.
Defined by the equation ______________.
y-axis
Even and Odd Functions An even function
is: Symmetric with
respect to the ______________.
Defined by the equation ______________.
An odd function is: Symmetric with
respect to the ______________.
Defined by the equation ______________.
y-axis
)()( xfxf
Even and Odd Functions An even function
is: Symmetric with
respect to the ______________.
Defined by the equation ______________.
An odd function is: Symmetric with
respect to the ______________.
Defined by the equation ______________.
y-axis origin
)()( xfxf
Even and Odd Functions An even function
is: Symmetric with
respect to the ______________.
Defined by the equation ______________.
An odd function is: Symmetric with
respect to the ______________.
Defined by the equation ______________.
y-axis origin
)()( xfxf )()( xfxf
Determine whether each function is even, odd, or neither.
64 xxxf
Determine whether each function is even, odd, or neither.
64 xxxf
648333 64 f
Determine whether each function is even, odd, or neither.
64 xxxf
648333 64 f
648333 64 f
Determine whether each function is even, odd, or neither.
64 xxxf
648333 64 f
648333 64 f
Determine whether each function is even, odd, or neither.
52 33 xxxf
Determine whether each function is even, odd, or neither.
52 33 xxxf
10823232 52 f
Determine whether each function is even, odd, or neither.
52 33 xxxf
10823232 52 f
8423232 52 f
Determine whether each function is even, odd, or neither.
52 33 xxxf
10823232 52 f
8423232 52 f
Determine whether each function is even, odd, or neither.
xxxf 3
Determine whether each function is even, odd, or neither.
xxxf 3
130555 3 f
Determine whether each function is even, odd, or neither.
xxxf 3
130555 3 f
130555 3 f
Determine whether each function is even, odd, or neither.
xxxf 3
130555 3 f
130555 3 f
PracticeDescribe the shifts in the graph of the function from the parent function of . State the coordinates of the vertex point of the graph. Determine if the function is odd, even, or neither and justify your answer.
13 2 xxf 2xxf