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Mastering Exponential Functions: Key Features Graphing

Learn to graph, interpret, & apply key features of exponential functions. Understand domain, range, end behavior, & essential vocabulary. Practical examples guide your understanding.

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Mastering Exponential Functions: Key Features Graphing

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  1. Lesson 3.6b Graphing & Identifying Key Features of Exponential Functions Concept: Characteristics of Exponential Functions Lesson EQ: How do you graph, interpret, and apply the key features of an exponential function? (Standard F.IF.4,5,7) Vocabulary: Domain, Range, & End Behavior

  2. Exponential Functions Recall General form a = initial value that determines the shape a > 1 stretch; 0 < a < 1 shrink; -a = reflection b = growth if the value is > 1 b = decay if the value is between 0 and 1 k = horizontal asymptote & vertical shift

  3. Guided Practice: Example 1, continued Complete the table of values to create a graph of the function. 3.4.2: Graphing Exponential Functions

  4. Domain The collection of all x-values (inputs). For exponential functions the domain will always be all real numbers . Example: Domain = all real numbers because any number can be used as x.

  5. Range The collection of all y-values (outputs). +a: Range is all numbers > asymptote. -a: Range is all numbers < asymptote. Example: Domain = all numbers > asymptote. y > 0

  6. End Behavior What happens at the ends of the graph. Exponential functions have 2 end behaviors. One towards + or - infinity and one towards the horizontal asymptote. Example: Left: As x -∞, y 0 Right: As x +∞, y +∞

  7. Guided Practice: Example 2, continued Complete the table of values to create a graph of the function. 3.4.2: Graphing Exponential Functions

  8. Example 2: Recall • Not a reflection • Decay • Horizontal Asymptote: y = 0 • y-intercept: (0, 1) • Domain = _____________ • Range = all numbers ____ asymptote y ____ _____ • End behavior: Left: As x-∞, y ___ Right: As x+∞, y ___

  9. Guided Practice: Example 3, continued Complete the table of values to create a graph of the function. 3.4.2: Graphing Exponential Functions

  10. Example 3: • Domain = _____________ • Range = all numbers ____ asymptote y ____ _____ • End behavior: Left: As x-∞, y ___ Right: As x+∞, y ___ Recall • Not a reflection • Growth • Horizontal Asymptote: y = 1 • y-intercept: (0, 2)

  11. Guided Practice: Example 4, continued Complete the table of values to create a graph of the function. 3.4.2: Graphing Exponential Functions

  12. Example 4: • Domain = _____________ • Range = all numbers ____ asymptote y ____ _____ • End behavior: Left: As x-∞, y ___ Right: As x+∞, y ___ Recall • Reflection • Decay • Horizontal Asymptote: y = 3 • y-intercept: (0, 2)

  13. Summarizing Strategy: Example for Absent friend Your absent friend needs you to show them an example of what they missed. Choose 3 of the following 5 features to identify for this exponential function: f(x) = 3x – 2 • Asymptote • y-intercept • Domain • Range • End Behavior

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