Math 3
2-3 Vertical Translations Part 2
Name_______________________________
In this investigation, we will be working towards the following learning goals:


I can translate functions vertically, both graphically and algebraically
I can apply knowledge of vertical translations to problem situations
In numbers 1-4, let f  x  be the original function
Let g  x  be a vertical translation up 4 units; let h  x  be a vertical translation down 6 units.
Given f  x  below, write the equations of g  x  and h  x  .
1.
f  x   3  2x 
g  x 
h  x 
2.
f  x   2 x2  4x
g  x 
h  x 
3.
f  x 
g  x 
h  x 
4.
f  x   x2  4x  6
g  x 
h  x 
4
x2
In numbers 5 and 6 let f  x  be the original function.
Let g  x  be a vertical translation up 2 units; let h  x  be a vertical translation down 3 units.
Given f  x  below, sketch graphs of g  x  and h  x  as accurately as possible.
5.
7.
6.
Write a coordinate translation rule that could be used to find h  x  in problem 5. That is, if you
were looking at a table of f ( x) , what would you do to each  x, y  value to create the table for
h  x .
g ( x) :
 x, y  
h( x) :  x, y  
8.
The dashed graph below is f  x  and the solid graph is g x , a vertical translation of f x  . Write
the equation of g  x  in terms of f  x  .
g  x 
9.
b.
Locate the local maximum and minimum points of each function and fill in the table below. How
is the x-coordinate for f(x) related to the x-coordinate for g(x) and for h(x)? How is the
y-coordinate for f(x) related to the y-coordinate for g(x) and for h(x)?
Local Maximums
Graph
Coordinate
(x, y)
Relationship between coordinates?
f(x)
g(x)
h(x)
_______________________________
Local Minimums
Graph
Coordinate
(x, y)
_______________________________
______________________________
f(x)
g(x)
h(x)
_______________________________
_______________________________
c.
Locate the y-intercept of each function and fill in the table below. How is the y-coordinate for g(x)
related to the y-coordinate for f(x)? How is the y-coordinate for h(x) related to the y-coordinate for
f(x)?
y-intercept
Graph
Coordinate
(x, y)
f(x)
g(x)
Relationship between coordinates?
h(x)
_________________________________
_________________________________
___________________________________________________________________________________
___________________________________________________________________________________
d.
Locate the zeroes of each function and fill in the table below. Is there a relationship between the
zeroes of f(x) and the zeroes of the translated functions?
Zeroes
Graph
Coordinate
(x, y)
f(x)
Relationship between coordinates?
g(x)
 2,0
1,0
 4, 0 
10.
h(x)
_______________________________
_______________________________
_______________________________
_______________________________
Below are vertical translations of parent functions. Write the equation of each function.
f ( x )  _______________
g ( x )  _______________
11.
Let’s generalize our knowledge about vertical translations.
When g  x   f  x   k , the y-intercept of g  x  ____________________________________
_____________________________________________________________________________
When g  x   f  x   k , the local maximum(s)/minimum(s) of g  x  ___________________
_____________________________________________________________________________
When g  x   f  x   k , the x-intercept(s) of g  x  ___________________________________
_____________________________________________________________________________
12.
b.
New exponential regression equation: y =
c.
Why did we subtract 35 from the data and then find a new regression equation? What was the
purpose of subtracting 35?
d.
Based on the equation you developed in part (b), come up with an exponential function that
models the original data. Think about how you would do this in terms of what we have learned
in this activity!
y=