f(𝑥)=log2(10−2𝑥)

Give the domain of the function 𝑓(𝑥) in interval notation.
Domain:

Give the range of the function 𝑓(𝑥) in interval notation.
Range:

To determine the **domain** and **range** of the function \( f(x) = \log_2(10 - 2x) \), let’s analyze both.

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### 1. Domain:
The domain is the set of all \( x \)-values for which the function is defined. For a logarithmic function, the argument inside the logarithm must be **strictly positive**.

\[
10 - 2x > 0
\]

Solve for \( x \):

\[
-2x > -10 \quad \Rightarrow \quad x < 5
\]

Thus, the domain of \( f(x) \) is all \( x \)-values less than 5.

**Domain in interval notation:**

\[
(-\infty, 5)
\]

---

### 2. Range:
A logarithmic function with any positive base (like \( \log_2 \)) has a **range of all real numbers**. 

Thus:

**Range in interval notation:**

\[
(-\infty, \infty)
\]

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### Final Answer:
- **Domain:** \( (-\infty, 5) \)  
- **Range:** \( (-\infty, \infty) \)

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Would you like a graph or further elaboration on these points?  

Here are five related questions you might find useful:  
1. What happens to the function as \( x \) approaches 5 from the left?  
2. How does the base of the logarithm affect the shape of the function?  
3. What is the behavior of \( f(x) \) as \( x \to -\infty \)?  
4. What is the value of \( f(x) \) at \( x = 0 \)?  
5. How does the function transform if the base changes to \( \log_{10}(10 - 2x) \)?  

**Tip:** When working with logarithmic functions, always ensure the argument is positive for the function to be defined.

f(x) = log2(10 - 2x)

Give the domain of the function f(x) in interval notation.
Domain:

Give the range of the function f(x) in interval notation.
Range:

Learn how to find the domain and range of the logarithmic function f(x) = log2(10 - 2x). This problem involves logarithmic functions and inequalities. Understand the conditions for the domain and explore the range of the function, suitable for Grades 9-12 students.

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