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A1 11 functions
1.
Functions
Evaluating Domain and Range Sequences
2.
Function Notation: f(x)
_ is the input f is the This does name of NOT mean the function f ____ x f(x)
3.
Function Notation: f(x)
x is the input f is the This does name of NOT mean the function f ____ x f(x)
4.
Function Notation: f(x)
x is the input f is the This does name of NOT mean the function f times x f(x)
5.
Evaluating functions
6.
Domain If a function
is undefined for any input, we say that number is not in the domain of the function.
7.
What is the
domain and range of this function? y = 2x + 1
8.
What is the
domain and range of this function? Scatter plot
9.
What is the
domain and range of this function? y = sin x
10.
Sequences Domain = Set
of Natural numbers
11.
Sequences Usually some kind
of pattern…
12.
5, 10, 15,
20, … What comes next?
13.
5, 10, 15,
20, 25 This is called an arithmetic sequence. “Arithmetic” sequences add the same number every time to the previous number.
14.
5, 10, 15,
20, 25 We can define this sequence with an equation: f(xn) = xn-1 + 5
15.
Can you write
an arithmetic sequence that starts with -2 and adds 3 each time?
16.
2, 4, 8,
16, … What comes next?
17.
2, 4, 8,
16, 32 This is called a geometric sequence. “Geometric” sequences multiply the same number to the one before.
18.
2, 4, 8,
16, 32 We can define this sequence with an equation: f(xn) = 2(xn-1)
19.
Can you write
a geometric sequence that starts with ¼ and multiplies by 2 each time?
Notas del editor
Ask students why they think that.
WAIT BEFORE NEXT SLIDE!!Ask how it can be written as an equation using domain first.
Ask students why they think that.
WAIT BEFORE NEXT SLIDE!!Ask how it can be written as an equation using domain first.
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