Warm-Up
Is the assignment of students to their mothers an example of a function? Explain.
Vocabulary
Independent variable
Dependent variable
Function rule
Function notation
Another Way to Think of Functions
We can think of a function like a machine. When we put something into it, the machine will perform a certain operation (or combination of operations) on it and produce an output.
We say the output is a function of the input, x, so we abbreviate it
“f of x,” or f(x).
You may also think of the f(x) values as the y-values.
The operation (or combination of operations) that the function machine performs on the input (xvalues) is known as the function rule.
The x-values (inputs) are called the independent variables .
The f(x), or y-values (outputs), are called the dependent variables , because they depend on what you put in for x.
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At this point, we have many names for the variables of a function:
Independent Variable x-values domain input x
Dependent Variable y-values range output f(x) f(x) is read, “f of x.” f(4) is read, “f of 4,” and it means to plug in 4 for x. Model Problem a) If f(x) = 2x + 3, find f(4).
Think of a function machine that uses the rule f(x) = 2x + 3.
For example, when the input x = 4 is given, the machine plugs in 4 for x. The output f(4) = 11 is produced since 2(4) + 3 = 11. b) Given the domain {4, 6, 8}, find the range.
Express the function as a set of ordered pairs.
Domain
4 f(x) = 2x + 3 Range
2(4) + 3 11
Ordered
Pairs
(4, 11)
Domain = {4, 6, 8}
Range = ________________________
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Exercise
1) If f(x) = 3x – 1, find: a) f(8) c) f(2) b) f(-1) d) f(0)
2) Given that f(x) = x + 4, find a value of x such that f(x) = 11.
3) Based upon the graph below, what is the value of f(1)?
Domain
-2
0
2
3
5)
4) Using the function rule f(x) = x 2 + 3 and the domain given, find the range.
Express the function as a set of ordered pairs. y = x 2 + 3 Range Ordered pairs
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Level B: Understanding Function Notation
Summary
Independent Variable x-values
Domain
Input x
Dependent Variable y-values range
Output f(x)
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#8:
Independent Practice/Homework – Day 5
In #1-6, write an expression for each function using f(x) notation. Then find f(5).
7.
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9)
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