6. Function notation Here are 3 curves and
their equations.
Write them in function
notation.
𝑦 = 𝑥3 + 2𝑥2 − 1 𝑦 = 𝑥2 − 3
𝑦 =
1
𝑥
+ 2
7. Function notation Here are 3 curves and
their equations.
Write them in function
notation.
𝑦 = 𝑥3 + 2𝑥2 − 1 𝑦 = 𝑥2 − 3
𝑦 =
1
𝑥
+ 2
𝑓(𝑥) = 𝑥3
+ 2𝑥2
− 1
8. Function notation Here are 3 curves and
their equations.
Write them in function
notation.
𝑦 = 𝑥3 + 2𝑥2 − 1 𝑦 = 𝑥2 − 3
𝑦 =
1
𝑥
+ 2
𝑓(𝑥) = 𝑥3
+ 2𝑥2
− 1 𝑓(𝑥) =
1
𝑥
+ 2
9. Function notation Here are 3 curves and
their equations.
Write them in function
notation.
𝑦 = 𝑥3 + 2𝑥2 − 1 𝑦 = 𝑥2 − 3
𝑦 =
1
𝑥
+ 2
𝑓(𝑥) = 𝑥3
+ 2𝑥2
− 1 𝑓(𝑥) =
1
𝑥
+ 2 𝑓 𝑥 = 𝑥2 − 3
10. Function notation
We can also describe
function in words:
𝑓 𝑥 = 𝑥2
− 3 “f of 𝑥 is 𝑥 squared subtract 3.”
11. Function notation
𝑓 𝑥 = 𝑥2
− 3
𝑓 2 = (2)2− 3 = 1
“f of 𝑥 is square and subtract 3.”
Function notation
makes it clear what we
are substituting :
12. Function notation
𝑓 𝑥 = 𝑥2
− 3
𝑓 1 = (1)2− 3 = -2
𝑓 2 = (2)2− 3 = 1
“f of 𝑥 is square and subtract 3.”
Function notation
makes it clear what we
are substituting :
30. Translating functions
Given that f(𝒙) = 𝒙𝟐
𝒚 = f(𝟒) + 2 = (𝟒)𝟐 + 2 = 18
Let 𝒚 = f(𝒙) + 2
What is 𝒚 if 𝒙 = 4?
Now let 𝒚 = f(𝒙 + 𝟐)
What is 𝒚 if 𝒙 = 4?
Function notation
31. Translating functions
Given that f(𝒙) = 𝒙𝟐
𝒚 = f(𝟒) + 2 = (𝟒)𝟐 + 2 = 18
Let 𝒚 = f(𝒙) + 2
What is 𝒚 if 𝒙 = 4?
Now let 𝒚 = f(𝒙 + 𝟐)
What is 𝒚 if 𝒙 = 4?
𝒚 = f(𝟒 + 𝟐) = (𝟔)𝟐 = 36
Function notation
32. Translating functions
Given that f(𝒙) = 𝒙𝟐
𝒚 = f(𝟒) + 2 = (𝟒)𝟐 + 2 = 18
Let 𝒚 = f(𝒙) + 2
What is 𝒚 if 𝒙 = 4?
Now let 𝒚 = f(𝒙 + 𝟐)
What is 𝒚 if 𝒙 = 4?
𝒚 = f(𝟒 + 𝟐) = (𝟔)𝟐 = 36
So, 𝑦 = f(𝒙 + 𝟐) ⇒ 𝑦 = (𝒙 + 𝟐)𝟐
Function notation
49. Quadratic functions
Now compare with
the equations.
2
0
−3
0
4
0
−5
0
y = 𝒙𝟐
y = (𝒙 − 𝟐)𝟐
y = (𝒙 − 𝟒)𝟐
y = (𝒙 + 𝟑)𝟐
y = (𝒙 + 𝟓)𝟐
What do you
notice?
50. Quadratic functions
Units moved is the
same as the number
in the bracket
but the sign is
opposite.
2
0
−3
0
4
0
−5
0
y = 𝒙𝟐
y = (𝒙 − 𝟐)𝟐
y = (𝒙 − 𝟒)𝟐
y = (𝒙 + 𝟑)𝟐
y = (𝒙 + 𝟓)𝟐
55. Quadratic functions
Transformations of y = 𝒙𝟐
Equation Transformation Comment
y = 𝒙𝟐 + a Translation by
𝑎
0
Translate in y direction.
Up if a positive.
Down if a negative.
The same as you see.
y = (𝒙 + 𝒂)𝟐
Translation by
0
−𝑎
Translate in x direction.
Left if a positive.
Right if a negative.
The opposite to what you see.
60. Quadratic functions
1. 2.
3. 4.
What are the
equations of
these curves?
y = (𝒙 − 𝟏)𝟐 y = (𝒙 + 𝟏)𝟐
y = 𝒙𝟐 -1 y = 𝒙𝟐
+2
61. Translating functions
Equation Transformation Comment
y = f(𝒙)+ a Translation by
𝑎
0
Translate in y direction.
Up if a positive.
Down if a negative.
The same as you see.
y = f(𝒙 + 𝒂) Translation by
0
−𝑎
Translate in x direction.
Left if a positive.
Right if a negative.
The opposite to what you see.
Transformations of y = f(𝒙)