https://file.aiquickdraw.com/mathbot/file/172607355877155p31wb1.jpg

The function provided is a piecewise function \( g(x) \) defined as follows:

\[
g(x) =
\begin{cases}
2x & \text{if } x < 6 \\
x - 1 & \text{if } x \geq 6
\end{cases}
\]

This function has two parts:

1. **For \( x < 6 \):** \( g(x) = 2x \)
2. **For \( x \geq 6 \):** \( g(x) = x - 1 \)

The function evaluates differently depending on whether \( x \) is less than 6 or greater than or equal to 6.

### For \( x = 6 \):

There is a specific note that at \( x = 6 \), the function uses the expression \( g(6) = 6 - 1 = 5 \), coming from the condition \( x \geq 6 \).

Let me know if you'd like further clarification or details about any specific aspect of this function!

### Five Related Questions:
1. What is the value of \( g(x) \) when \( x = 5 \)?
2. How do we graph this piecewise function?
3. Is this function continuous at \( x = 6 \)?
4. What happens to \( g(x) \) as \( x \to \infty \)?
5. How do you calculate the derivative of \( g(x) \) for \( x < 6 \) and \( x \geq 6 \)?

**Tip:** When dealing with piecewise functions, always check for continuity at the boundaries between pieces (in this case, at \( x = 6 \)).

Learn how to evaluate the piecewise function g(x) defined as 2x for x < 6 and x - 1 for x ≥ 6. This example covers key topics like piecewise functions and checking continuity at x = 6. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation