Graphing Exponential Functions

Study sheet excerpt

Course Outline

  1. Exponential Function Foundations
  2. Graphs of Growth and Decay
  3. Transformations of Exponential Graphs
  4. Exponential Growth Models
  5. Exponential Decay Models
  6. Applications of Exponential Functions
  7. Analyzing Function Properties
  8. Piecewise and Comparative Graphs

1. Exponential Function Foundations

Key Concepts & Definitions

  • Exponential function : has the form f(x)=bxf(x)=b^x, where b is a positive constant and x is the exponent

★ Must-know

📌 For y=abxy=ab^x with a>0, the function represents exponential growth when b>1 and exponential decay when 0<b<1.

Further detail

📌 When b=1, y=abxy=ab^x is constant rather than exponential growth or decay, and a negative base does not produce a real-valued function for every real x.

Memory Hook

Growth has b > 1, whereas decay has 0 < b < 1.

2. Graphs of Growth and Decay

Essential Points

  • The graph of f(x)=2xf(x)=2^x has domain all real numbers, range all positive real numbers, y-intercept (0,1), and horizontal asymptote y=0.
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Quiz preview

1. Which expression defines an exponential function in which the variable appears as an exponent?

2. What is the general form of an exponential function?

3. For y=5bxy=5b^x, which condition on the positive base bb indicates exponential decay?

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Flashcards preview

What is the form of an exponential function?

An exponential function has the form f(x)=bxf(x)=b^x with positive base bb.

Exponential function symbol

f(x)=b^x, with b > 0

When does y=abxy=ab^x represent exponential growth?

It represents exponential growth when b>1b>1 and a>0a>0.

Growth condition on b

b > 1 for growth, 0<b<1 for decay

What is the domain of the graph of f(x)=2xf(x)=2^x?

All real numbers.

Graph of f(x)=2^x

Domain all reals; y-intercept (0,1); asymptote y=0

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Frequently asked questions

What does the study sheet on Graphing Exponential Functions cover?

The study sheet covers the essential concepts of Graphing Exponential Functions. It is organized by topic to facilitate learning and memorization, with key definitions, explanations and summaries.

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How many questions are in the Graphing Exponential Functions quiz?

The quiz contains 10 multiple-choice questions with detailed corrections and explanations for each answer. Ideal for testing your knowledge and identifying gaps.

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How to study Graphing Exponential Functions with flashcards?

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