TACKLING TRANSLATIONS
Translating Graphs of Functions - shifting a graph along the x or y-axis (vertically or
horizontally).
Which variable controls changes along the x-axis?
Which variable controls changes along the y-axis?
How do we translate graphs?
-
The input of a function is the variable that is used to find the output of an equation. The
input is usually found in the equation.
-
The output of a function is the result of plugging a number into an equation. The output is
usually found by itself on one side of the equation and has been solved for in terms of the
input variable.
***The output of a function is represented by f(input variable) which is said to be “f of a” if
a were the input variable.
Ex:
An equation of a line in slope-intercept form is:_____________
What is the input of this equation?
What is the output of this equation?
Write the equation of a line in the form of a function:_____________
*Therefore, f(x) represents the variable ___ when graphing a function.
In order to shift a graph along either axis, we need to replace the variables with different
“instructions”.
A.
Applying translating to equations:
If we add to the x-variable (or input), the graph will move ________.
If we subtract from the x-variable (or input), the graph will move ________.
If we add to the y-variable (or output), the graph will move ________.
If we subtract from the y-variable (or output), the graph will move ________.
B.
Applying translating to a function:
To translate a function in the form f(x), we need to replace the input and the output with different
“instructions”.
Direction
Number
Variable
f(x+2) will move the graph
_______ for ______ on the _______ axis.
f(x-9) will move the graph
_______ for ______ on the _______ axis.
f(x)-8 will move the graph
_______ for ______ on the _______ axis.
f(x)+3 will move the graph
_______ for ______ on the _______ axis.
Write the directions for translating a graph up 3 and left 2: __________________
C.
Writing the equation for a translated function:
1)
When translating a function or equation of a line, we are first given an equation or
function to translate.
f(x) = x + 5
2)
y=x+5
Next, we are given instructions to tell us how the graph will move.
Left 2, Up 3
3)
or
or
f(x + 2) - 3
Then, we replace the input and output (or variables) with the proper instructions.
(y – 3) = (x + 2) + 5
4)
Finally, we solve for the output variable.
y–3=x+2+5
y–3=x+7
y–3+3=x+7+3
y = x + 10
Bonus Page:
What is unique about a line with a slope of one when it is translated? (Hint: Use your calculator
to graph an equation. Then, translate it. Which axis did it move on?)
What happens if you want to translate a line with slope 1 along both the x and y-axis the same
distance? (Hint: Graph y = x and translate it the same distance on both the x and y axis.)
Why doesn’t this work if the slope is not 1?
Why doesn’t this work if the graph is not a line?