📚 Topic Summary
Exponential functions are a crucial part of Algebra 2. They describe situations where a quantity increases or decreases at a constant percentage rate over equal intervals. Identifying them involves recognizing the characteristic form $f(x) = ab^x$, where $a$ is the initial value, and $b$ is the growth/decay factor. The key is that the variable, $x$, is in the exponent. Constant differences between $x$-values correspond to constant ratios between $f(x)$-values.
This worksheet tests your knowledge on the vocabulary, characteristics and applications of exponential functions. By completing these activities you should become much more familiar with the topic!
🧮 Part A: Vocabulary
Match the following terms with their definitions:
- Term: Exponential Function
- Term: Growth Factor
- Term: Decay Factor
- Term: Initial Value
- Term: Asymptote
- Definition: The horizontal line that a graph approaches but never touches.
- Definition: A function where the independent variable is in the exponent.
- Definition: The value of a function when the input is zero.
- Definition: The factor by which a quantity increases.
- Definition: The factor by which a quantity decreases.
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✍️ Part B: Fill in the Blanks
An exponential function has the general form $f(x) = ab^x$, where $a$ represents the ________ and $b$ is the ________. If $b > 1$, the function represents exponential ________. If $0 < b < 1$, the function represents exponential ________. The ________ is a horizontal line that the exponential function approaches.
🤔 Part C: Critical Thinking
Explain how you can determine if a table of values represents an exponential function. Include examples of how the values change with respect to x.
