Alg II Chapter 2 Notes.notebook 1 September 19, 2016 Algebra II Chapter 2: Linear Equations and Functions Vocabulary Chapter 2 Lesson 1 Represent Relations and Functions
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Alg II Chapter 2 Notes.notebook
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September 19, 2016
Algebra IIChapter 2:
Linear Equations and Functions
Vocabulary
Chapter 2 Lesson 1Represent Relations and Functions
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Example 1: Represent Relations
Example 2: Identifying Functions
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Example 3: Use the Vertical Line Test
Example 4: Graph an Equation in Two Variable
YOU choose the x values!!! Then, substitute them to find the corresponding y values!
State the domain and range.GRAPH THE PARENT FUNCTION!
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Example 5: Classify and Evaluate Functions
Note: Linear functions do not have variable exponents greater than 1! They also do not have variables in the denominators of fractions.
By the way... f(x) is read as "the value of function f at x" or "f of x"
Example 6: Use a Function in Real Life
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Chapter 2 Lesson 2Find Slope and Rate of Change
Vocabulary
They will have equivalent slopes.
Reciprocal? What is that?
They will have slopes that are opposite reciprocals of each other.
Example 1: Find Slope in Real Life
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Example 2: Standardized Test Prep
Slope Formula: Slope is the change in y over the change in x!
Example 3: Classify Lines Using Slope
Slope Formula:
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Example 4: Classify Parallel and Perpendicular Lines
Slope Formula:
Find the slopes and compare!
Example 5: Solve a MultiStep Problem
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Chapter 2 Lesson 3Graph Equations of Lines
Vocabulary
Example 1: Graph Linear Functions
YOU MUST ALWAYS GRAPH THE PARENT FUNCTION!!!!
1. Graph the parent function.2. Make a table of values.3. Plot the points.4. Draw a line through the points.
State the domain and range.
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Example 2: Graph an Equation in SlopeIntercept FormYOU MUST ALWAYS GRAPH THE PARENT FUNCTION!!!!
State the domain and range.. GRAPH THE PARENT FUNCTION!
Example 3: Solve a MultiStep Problem
State the domain and range.
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Example 4: Graph an Equation in Standard Form
GRAPH THE PARENT FUNCTION! State the domain and range.
Example 5: Graph Horizontal and Vertical Lines
The slope is zero!The slope is undefined!
State the domain and range.
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Chapter 2 Lesson 4Write Equations of Lines
Vocabulary
Example 1: Write an Equation Given the Slope and yintercept
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Example 2: Write an Equation Given the Slope and a Point
Example 3: Write Equations of Parallel and Perpendicular LinesReminder:Parallel slopes are equalPerpendicular slopes are opposite reciprocals
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Example 4: Write an Equation Given Two Points
Example 5: Write a Model Using SlopeIntercept Form
State the domain and range.
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Example 6: Write a Model Using Standard Form
Chapter 2 Lesson 7Use Absolute Value Functions and Transformations
Vocabulary
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Steps:1. Identify and plot the vertex. Identify the
line of symmetry. Reminder: h=horizontal move and k=vertical move AND the h position sign will change
2. Make a table. (You choose x values.)3. Plot the points.4. Use symmetry to plot more points.5. Connect the points with a Vshaped graph.
Example 1:
ALWAYS GRAPH THE PARENT FUNCTION!State the domain and range.
Example 2:
Steps:1. Identify and plot the vertex. Identify the
line of symmetry. Reminder: h=horizontal move and k=vertical move AND the h position sign will change
2. Identify if the graph with stretch or shrink and if it will open up or down. Make a table.
3. Plot the points.4. Use symmetry to plot more points.5. Connect the points with a Vshaped graph.
ALWAYS GRAPH THE PARENT FUNCTION!
If a is positive, the graph will open up.If a is negative, the graph will open down.
State the domain and range.
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Example 3:
ALWAYS GRAPH THE PARENT FUNCTION!
Steps:1. Identify and plot the vertex. Identify the
line of symmetry. Reminder: h=horizontal move and k=vertical move AND the h position sign will change
2. Identify if the graph with stretch or shrink and if it will open up or down. Make a table.
3. Plot the points.4. Use symmetry to plot more points.5. Connect the points with a Vshaped graph.
If a is positive, the graph will open up.If a is negative, the graph will open down.
State the domain and range.
Example 4: Write an Absolute Value Function
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Example 5: Apply Transformations to a Graph
Chapter 2 Lesson 8 Graph Linear Inequalities in Two Variables
Vocabulary
The shaded region in the graph above is a "halfplane".
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Example 1: 1. Substitute the ordered pair values into the inequality.2. Evaluate each side.3. Determine if the statement is true or not true.
*If the statement is true, the ordered pair is a solution. *If the statement is NOT true, the ordered pair is not a solution.
Example 2:
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Example 3:
Example 5: Graphing an Absolute Value Inequality
1. Graph the equation of the boundry line. Decide if it needs to be dashed or solid.
2. Use a test point to determine which side to shade.*If the statement is true, the ordered pair is a solution. *If the statement is NOT true, the ordered pair is not a solution.
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