Math Problem Statement
Solution
Based on the uploaded problem:
- Graph Type: Exponential function.
- Horizontal Asymptote: A dashed line is shown, which indicates the graph approaches but does not touch this line.
Step 1: Domain
The domain of an exponential function is all real numbers, because you can input any -value into the exponential function, and it will yield a corresponding -value.
- Domain: or "All reals."
Step 2: Range
The graph of an exponential function typically approaches a horizontal asymptote but never crosses it. Based on the graph:
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The horizontal asymptote is at , meaning the function never reaches or dips below .
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The -values are strictly greater than 0 ().
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Range: .
Final Answer:
(a) Range:
(b) Domain:
Would you like further clarification or examples of similar problems?
Here are 5 related questions for further exploration:
- How would the graph change if the asymptote moved to ?
- What is the range and domain of a logarithmic function?
- How do transformations (shifts, stretches, reflections) affect the domain and range of an exponential function?
- How do we identify the asymptote of an exponential function algebraically?
- Can an exponential function have a range that includes negative values?
Tip: Always verify the asymptote and direction of the graph before determining range.
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Math Problem Analysis
Mathematical Concepts
Exponential Functions
Domain and Range
Asymptotes
Formulas
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Theorems
Exponential Function Properties
Range and Domain of Functions
Suitable Grade Level
Grades 9-12
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