Aim #67: How do we translate the graph of y = x2 and y = |x|?
Homework: Handout
Do Now:
Describe the translation that moves the
parent function y = x2 to the new graph.
What do you think the new equation
would be?
Graph the following 3 functions on the given set of axes and then answer the
questions that follow.
f(x) = |x|
g(x) = |x - 3|
h(x) = |x + 2| - 4
How was g(x) translated in comparison to f(x)?
How was h(x) translated in comparison to f(x)?
Can we come up with a rule for shifting any function in the horizontal and vertical
direction?
A Translation is a slide (right or left, up or down)
T-2, 3 means _______________________
The rule for writing the equation after a translation Ta, b is replace x with x - a
and replace y with y - b or
x
y
x-a
y-b
Determine the equation of the following functions after the given translations:
1. y = x2 T2,­1
2. y = |x| 2 ­ 5 3. y = (x ­ 3)
T3,7
T­2,0
4. y = |x ­ 2| + 3
T4,3
T2,­3
5. y = (x + 1) ­ 3 2
6. y = f(x) T­4,2
Directions for #s 1-4:
a) Write the equation of the function after the given translation.
b) Graph the function.
c) State the domain and range.
Sum It Up!!
Given a parent function f(x) then:
y = f(x - h): translates h units to the right
y = f(x + h): translates h units to the left
y = f(x) + k : translates k units up
y = f(x) - k : translates k units down