https://file.aiquickdraw.com/mathbot/file/1727150263037wak2jdc6.jpg

This is a piecewise function \( f(x) \), where the value of the function depends on whether \( x \) is less than or equal to 4 or greater than 4. The function is defined as:

\[
f(x) = \begin{cases} 
5 & \text{if } x \leq 4 \\
4x - 6 & \text{if } x > 4 
\end{cases}
\]

Now, let's evaluate the function for each value provided:

1. \( f(-5) \): Since \( -5 \leq 4 \), use the first case, \( f(x) = 5 \).  
   So, \( f(-5) = 5 \).

2. \( f(0) \): Since \( 0 \leq 4 \), use the first case, \( f(x) = 5 \).  
   So, \( f(0) = 5 \).

3. \( f(4) \): Since \( 4 \leq 4 \), use the first case, \( f(x) = 5 \).  
   So, \( f(4) = 5 \).

4. \( f(5) \): Since \( 5 > 4 \), use the second case, \( f(x) = 4x - 6 \).  
   So, \( f(5) = 4(5) - 6 = 20 - 6 = 14 \).

5. \( f(7) \): Since \( 7 > 4 \), use the second case, \( f(x) = 4x - 6 \).  
   So, \( f(7) = 4(7) - 6 = 28 - 6 = 22 \).

The final answers are:

\[
f(-5) = 5, \quad f(0) = 5, \quad f(4) = 5, \quad f(5) = 14, \quad f(7) = 22
\]

Would you like more details on how piecewise functions work or any further clarifications?

Here are 5 questions to consider based on this problem:

1. What is a piecewise function, and how do you evaluate it?
2. What are the conditions that determine which part of the function to use?
3. How does the value of \( f(x) \) change as \( x \) crosses the boundary at \( x = 4 \)?
4. Can you describe a real-world scenario that could be modeled by this kind of function?
5. How would the function change if the condition \( x \leq 4 \) were instead \( x < 4 \)?

**Tip:** Always check the conditions of a piecewise function carefully before evaluating to ensure you are using the correct rule for each \( x \).

Evaluate the piecewise function f(x) = {5 if x <= 4, 4x - 6 if x > 4} for f(-5), f(0), f(4), f(5), and f(7).

This problem involves evaluating a piecewise function defined as f(x) = 5 for x <= 4 and f(x) = 4x - 6 for x > 4. Evaluate the function for x values of -5, 0, 4, 5, and 7. Learn how to apply piecewise functions step by step, suitable for Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation