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Lesson Plans and Worksheets for Algebra I
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More Lessons for Algebra I
Common Core For Algebra I
Examples, solutions, and videos to help Algebra I students learn how to understand that a function from one set (called the domain) to another set (called the range) assigns each element of the domain to exactly one element of the range and understand that if f is a function and x is an element of its domain, then f(x) denotes the output f of corresponding to the input x.
Students use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
Worksheets for Algebra I, Module 3, Lesson 9 (pdf)
Worksheets for Algebra I, Module 3, Lesson 10 (pdf)
Lesson 9
Function: A function is a correspondence between two sets, X and Y, in which each element of X is matched1to one and only one element of Y. The set X is called the domain of the function.
The notation f: X → Y is used to name the function and describes both X and Y. If x is an element in the domain X of a function f: X → Y, then x is matched to an element of Y called f(x). We say f(x) is the value in Y that denotes the output or image of f corresponding to the input x.
Range or Image of a Function: The range (or image) of a function f: X → Y is the subset of Y, denoted f(X), defined by the following property: y is an element of f(X) if and only if there is an x in X such that f(x) = y.
Equivalent Functions: Two functions, f: X → Y and g: X → Y, are said to be equivalent (and written f = g) if they have the same domain X, take values in the same set Y, and for each x in X, f(x) = g(x).
Identity: An identity is a statement that two functions are equivalent.
Example 3
Let X = {1, 2, 3, 4} and Y = {5, 6, 7, 8, 9} . f and g are defined below.
f: X → Y
f = {(1, 7), (2, 5), (3, 6), (4, 7)}
g: Y →X
g = {(6, 4), (7, 1), (8, 1), (9, 2)}
Is f a function? If yes, what is the domain and what is the range? If no, explain why f is not a function.
Is g a function? If yes, what is the domain and range? If no, explain why g is not a function. What is f(2)?
If f(x) = 7, then what might x be?
Lesson 9 Exit Ticket
Lesson 10 Student Outcomes
Lesson 10 Problem Set Sample Solutions
Lesson 10 Problem Set Sample Solutions
4. Provide a suitable domain and range to complete the definition of each function.
6. Given the function f whose domain is the set of real numbers, let f(x) = 1 if x is a rational number, and let f(x) = 0 if x is an irrational number.
Lesson 10 Exit Ticket
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