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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 the meaning of the graph of y = f(x), namely {(x, y) | x ∈ D and y = f(x)}. Students understand the definitions of when a function is increasing or decreasing.

### New York State Common Core Math Algebra I, Module 3, Lesson 12

Worksheets for Algebra I, Module 3, Lesson 12 (pdf)

• Students understand the definitions of when a function is increasing or decreasing.

Lesson 12 Exit Ticket

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

2. Let f(x) = -1/2 x + 2, for in the domain 0 ≤ x ≤ 4.

a. Write out in words the meaning of the set notation:

{(x, y) | 0 ≤ x ≤ 4 and y = f(x)}

b. Sketch the graph of y = f(x).

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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 the meaning of the graph of y = f(x), namely {(x, y) | x ∈ D and y = f(x)}. Students understand the definitions of when a function is increasing or decreasing.

Lesson 12 Student Outcomes

• Students understand the meaning of the graph of y = f(x), namely {(x, y) | x ∈ D and y = f(x)}.• Students understand the definitions of when a function is increasing or decreasing.

Lesson 12 Summary

Graph of y = f(x). Given a function f whose domain D and the range are subsets of the real numbers, the graph of y = f(x) is the set of ordered pairs (x, y) in the Cartesian plane given by

{(x, y) | x ∈ D and y = f(x)}

When we write {(x, y) | y = f(x)} for the graph of y = f(x), it is understood that the domain is the largest set of real numbers for which the function f is defined.

The graph of f is the same as the graph of the equation y = f(x).

Increasing/Decreasing. Given a function f whose domain and range are subsets of the real numbers and is an interval contained within the domain, the function is called increasing on the interval I if

f(x_{1}) < f(x_{2}) whenever x_{1} < x_{2} in I

It is called decreasing on the interval if

f(x_{1}) > f(x_{2}) whenever x_{1} > x_{2} in I

Example 1

In the previous lesson, we studied a simple type of instruction that computers perform called a for-next loop. Another simple type of instruction is an if-then statement.

Below is example code of a program that tests for and prints “True” when x + 2 = 4; otherwise it prints “False.”

Declare x integer

For all x from 1 to 4

If x + 2 = 4 then

Print True

else

Print False

End if

Next x

Example 2

Perform the instructions in the following programming code as if you were a computer and your paper was the computer screen:

Declare x integer

Initialize G as {}

For all x from 0 to 4

If x^{2} - 4x + 5 = 2 then

Append x to G

else

Do NOT x append to G

End if

Next x

Print G

Lesson 12 Exit Ticket

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

2. Let f(x) = -1/2 x + 2, for in the domain 0 ≤ x ≤ 4.

a. Write out in words the meaning of the set notation:

{(x, y) | 0 ≤ x ≤ 4 and y = f(x)}

b. Sketch the graph of y = f(x).

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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