Math 12 Chapter 1 Day 3 notes
Day 3Notes Sec 1.3Reflections:
Reflections over the x-axis:
In order to reflect ()x f y =
“y”is replaced with “-y ”
Example:()x f y =?or y reflect the original function over
the x-axis
Example:Use a table of values to graph 2x y ?=,then use your graphing calculator to check.Answer:
Example:Given ()x f y =,sketch ()
x f y ?=In other words,every y-value on the original function gets multiplied by -1
y Draw a table of values for 2
x y =?Multiply every y-value by -1
?Plot the new coordinates and sketch the new curve x 1y 1
12??=y y -2 4-4 -1 1-1 00011-1 24-4
does not change)
Answer:
Reflections over the y-axis:
In order to reflect ()x f y =over the y-axis,“x”is replaced with “-x ”Example:f y =function over the y-axis
Example:Use a table of values to graph ()2
x y ?=,then use your graphing calculator to check.Answer:
Example:Given ()x f y =,sketch ()
x f y ?=x
1y 1
12??=y y -3 1-1 -1 3-3 43
-3
In other words,every x-value on the original function gets multiplied by -1
y Draw a table of values for 2
x y =?Multiply every x-value by -1
?Plot the new coordinates and sketch the new curve 112??=x x x
y 2-2 41-1 1000-1 11-2 24
Answer:
Reflections over the
y =x axis:(Also known as graphing inverses)In order to reflect ()x f y =over the y =x axis,“x”and “y”are swapped
Example:()y f x =or ()x f y 1?=will reflect the original function over the y =x axis
Example:Use a table of values to graph the inverse of 2x y =,(the reflection of this curve in the y =x axis)then use your graphing calculator to check.Answer:
Example:Given ()x f y =,sketch ()
x f y 1?=1
12??=x x x
3-3 11-1 3-4
4
3
y y axis x =x ±=Draw a table of values for 2
x y =?Swap the x and y values of every coordinate
?Plot the new coordinates and sketch the new
curve
2x 1x 1y 2
y 4
-2 4 -2 1
-1 1 -1 000011114242
Answer:
Question:What point would be invariant for this particular reflection?
Answer:(3,3) notice that invariant points will always be found on the line of reflection
2x
1x 1y 2y
1 -3 1 -3 3 -1 3 -1 3 4 3 4