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Lesson Plans and Worksheets for Algebra I

Lesson Plans and Worksheets for all Grades

More Lessons for Algebra I

Common Core For Algebra I

Examples, solutions, and videos to help Algebra I students learn how to understand set builder notation for the graph of a real-valued function: {(x, f(x)) | x ∈ D} .

Students learn techniques for graphing functions and relate the domain of a function to its graph.

### New York State Common Core Math Algebra I, Module 3, Lesson 11

Worksheets for Algebra I, Module 3, Lesson 11 (pdf)

1. Perform the instructions for the following programming code as if you were a computer and your paper was the computer screen.

Declare x an integer

Let f(x) = 2x + 1

Initialize G as {}

For all x from -3 to 2

Append (x, f(x)) to G

Next x

Plot G

2. Write three or four sentences describing in words how the thought code works.

Lesson Plans and Worksheets for Algebra I

Lesson Plans and Worksheets for all Grades

More Lessons for Algebra I

Common Core For Algebra I

Examples, solutions, and videos to help Algebra I students learn how to understand set builder notation for the graph of a real-valued function: {(x, f(x)) | x ∈ D} .

Students learn techniques for graphing functions and relate the domain of a function to its graph.

Lesson 11 Summary

Graph of f: Given a function f whose domain D and the range are subsets of the real numbers, the graph of f is the set of ordered pairs in the Cartesian plane given by {(x, f(x)) | x ∈ D}

When we graph a function we want to think of "Input" and "Output"

Declare x an integer

Let
f(x) = 2x + 1

Initialize G as {}

For all x from -1 to 4

Append (x, f(x)) to G

Next x

Plot G

Declare x a real

Let
f(x) = 2x + 3

Initialize G as {}

For all x such that 2 ≤ x ≤ 8

Append (x, f(x)) to G

Next x

Plot G

Set Builder Notation

{(x, 2x + 1) | x is an integer,
-1 ≤ x ≤ 4}

{(x, 2x + 3) | x is real,
2 ≤ x ≤
8}

Exercise

4. Sketch the graph of the functions defined by the following formulas, and write the graph of f as a set using set-
builder notation.

(Hint: Assume the domain is all real numbers unless specified in the problem.)

f(x) = 1/2x - 5

f(x) = (x + 1)^{2} - x^{2},
-3 ≤ x ≤ 3

1. Perform the instructions for the following programming code as if you were a computer and your paper was the computer screen.

Declare x an integer

Let f(x) = 2x + 1

Initialize G as {}

For all x from -3 to 2

Append (x, f(x)) to G

Next x

Plot G

2. Write three or four sentences describing in words how the thought code works.

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