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 Module 3, Algebra I, Lesson 11

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Common Core For Algebra I

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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