Functions from a Calculus Perspective

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Functions from a Calculus Perspective by Mind Map: Functions from a Calculus Perspective

1. Functions

1.1. Use Set Builder Notation

1.2. Use Interval Notation

1.3. Identify Relations that are Functions

1.4. Find Function Values

1.5. Find Domains Algebraically

1.6. Piecewise-Defined Functions

2. Analyzing Graphs of Functions and relations

2.1. Estimate Function Values

2.2. Find Domain & Range

2.3. Find y-intercepts

2.4. Find Zeros

2.5. Test for Symmetry

2.5.1. Y-axis Symmetry Even Function

2.5.2. Origin Symmetry Odd Functions

2.5.3. X-axis Symmetry Even Functions

2.6. Identify Even & Odd Functions

3. Parent Functions and Transformation

3.1. Describe Characteristics of a Parent Function

3.2. Graph Translations

3.3. Write Equations for Transformations

3.4. Describe and Graph Transformations

3.5. Graph Piecewise-Defined Functions

3.6. Transformations of Functions

3.7. Describe and Graph Transformations

4. Continuity, End Behavior, and Limits

4.1. Identify Point of Continuity

4.2. Identify a Point of Discontinuity

4.3. Approximate Zeros

4.4. Graphs that Approach Infinity

4.5. Graphs that Approach a Specific Value

4.6. Apply End Behavior

4.7. Continuity Test

4.7.1. Continuous

4.7.2. Discontinuous Removable Nonremovable Infinity Jump

5. Inverse Relations and Functions

5.1. Apply the Horizontal Line Test

5.2. Find Inverse Functions Algebraically

5.3. Verify Inverse Functions

5.4. Find Inverse Functions Graphically

5.5. Use an Inverse Function

6. Extrema and average Rates of Change

6.1. Analyze Increasing and Decreasing Behavior

6.2. Estimate and Identify Extrema of a Function

6.3. Use a Graphing Calculator to Approximate Extrema

6.4. Use Extrema for Optimization

6.5. Find Average Rates of Change

6.6. Find Average Speed

7. Function Operations and Composition of Functions

7.1. Operations of Functions

7.2. Compose Two Functions

7.3. Find a Composite Function with a Restricted Domain

7.4. Decompose a Composite Function

7.5. Compose Real-World Functions