Math Problem Statement
Solution
The image shows the following mathematical statement in Arabic:
إذا كانت الدالة فإن مداها هو
Translation: "If the function is , then its range is ."
Explanation:
The given function is , which is an exponential function. However, the range provided here, , is incorrect for the actual exponential function .
The correct range of the function is: This is because is always positive for all real values of . Therefore, the range should be , not . The value 3 mentioned in the image might refer to a specific case or condition, but the general range is .
Would you like further details or clarification on exponential functions?
Here are five questions you might explore:
- What is the general behavior of exponential functions?
- How do exponential growth and decay differ?
- What is the domain of the function ?
- How does changing the base of the exponential function affect its range?
- How can exponential functions be used in real-world applications?
Tip: The base of an exponential function affects the rate of growth; larger bases result in faster increases.
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Math Problem Analysis
Mathematical Concepts
Exponential Functions
Function Range
Formulas
y = 3^x
Theorems
Exponential Growth Theorem
Suitable Grade Level
Grades 9-12