Math Problem Statement

إذا كانت الدالة y = 3^x فإن مداها هو {y | y ≥ 3}

Solution

The image shows the following mathematical statement in Arabic:

إذا كانت الدالة y=3xy = 3^x فإن مداها هو {yy3}\{y | y \geq 3\}

Translation: "If the function is y=3xy = 3^x, then its range is {yy3}\{y | y \geq 3\}."

Explanation:

The given function is y=3xy = 3^x, which is an exponential function. However, the range provided here, {yy3}\{y | y \geq 3\}, is incorrect for the actual exponential function y=3xy = 3^x.

The correct range of the function y=3xy = 3^x is: y>0y > 0 This is because 3x3^x is always positive for all real values of xx. Therefore, the range should be {yy>0}\{y | y > 0\}, not {yy3}\{y | y \geq 3\}. The value 3 mentioned in the image might refer to a specific case or condition, but the general range is y>0y > 0.

Would you like further details or clarification on exponential functions?

Here are five questions you might explore:

  1. What is the general behavior of exponential functions?
  2. How do exponential growth and decay differ?
  3. What is the domain of the function y=3xy = 3^x?
  4. How does changing the base of the exponential function affect its range?
  5. How can exponential functions be used in real-world applications?

Tip: The base of an exponential function axa^x 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