Questions/
Main Ideas:
ELL Algebra 1- Lesson 4
Notes
Name: ________________________
Period: _______Date: ___________
TOPIC: Function Translations and y-intercepts
The four functions given below are written in function notation .
For each one, fill in the table of values, then graph assuming they are continuous.
What is the
y-intercept of
a graph?
-What does continuous mean? _________________________________________________________
THEN, state the
y– intercept
-What is the y-intercept? _____________________________________________________________
f  x   2x
x
–3
f  x
x
–4
f  x
f  x   2x  3
f  x
x
–1
x
–5
–3
0
–3
0
–1
1
–2
2
0
3
0
3
2
4
1
y-intercept:_______
y-intercept:_______
f  x
y-intercept:_______
SIMILARITIES
What do all the function rules have in common?
DIFFERENCES
What is different among all function rules?
What do all the graphs have in common?
What is different among all graphs?
y-intercept of a How does the function rule define the y-intercept?
linear function
f  x   2x
Number without an “ x ”:__________
written in
function
notation
f  x   2x  4
–1
y-intercept: ______
What is a
coefficient?
f  x   2x  2
y-intercept: __________
f  x   2x  2
Number without an “ x ”:___________
y-intercept: __________
f  x   2x  3
Number without an “ x ”:___________
y-intercept: __________
f  x   2x  4
Number without an “ x ”:___________
y-intercept: __________
Do you see a pattern? _______________________________________________________________
CONCLUSIONS
Rules of
function
notation

(only for functions written _______________________________):
Two linear functions written in function notation that have the same coefficient of “ x ”
must always:

The number in the function rule that does not have an “ x ”____________________________
You try…
State the y-intercept of each of the functions below.
1. f  x   5x  1
2.
y-intercept: ______
f  x 
3
x3
4
3.
y-intercept:_______
f  x   7x 
1
2
4.
y-intercept:_______
f  x   9  5x
y-intercept:______
5. Which functions in problems 1 – 4 above would you expect to lean the same way? Why?
Let’s apply the rules we just learned to other functions that are not linear.
Below are graphs of functions
f  x  , g  x  , and h  x  .
Use the same y-intercept rule you just learned to draw the graph they ask for in each case below.
Draw f  x  1
Draw g  x   3
Draw h  x   4
g  x
f  x
h  x
So, for functions written in ____________________________ , we can say:
 Adding a number to the function will:
What is a
function
translation?

Subtracting a number from the function will:
To move a function like this on the coordinate plane is called a _____________________________.
Summary:
Name ___________________
QUIZ
N
f  x    2x
x
–3
f  x
f  x   3x  2
x
–4
f  x
f  x   3x  3
x
–1
f  x
f  x   3x  4
x
–5
–1
–3
0
–3
0
–1
1
–2
2
0
3
0
3
2
4
1
y-intercept: _____
y-intercept:_______
y-intercept:_______
f  x
y-intercept:_______