function
x + 1,
x≤ -2
j (x) =
12x2 + 3x - 20, x> -2

The function \( j(x) \) is piecewise, meaning it has different definitions depending on the value of \( x \). Here's how it's defined:

\[
j(x) = 
\begin{cases} 
x + 1 & \text{if } x \leq -2, \\
12x^2 + 3x - 20 & \text{if } x > -2.
\end{cases}
\]

This means:
- When \( x \) is less than or equal to \(-2\), you use the expression \( x + 1 \).
- When \( x \) is greater than \(-2\), you use the quadratic expression \( 12x^2 + 3x - 20 \).

Would you like a more detailed explanation of how this function behaves, or to explore specific values?

### Related questions:
1. How would you find \( j(x) \) at a specific value of \( x \)?
2. What is the domain of this piecewise function?
3. How do you graph a piecewise function?
4. What happens to \( j(x) \) as \( x \) approaches \(-2\) from both sides?
5. Can you find the roots of the quadratic part of the function?

**Tip**: When dealing with piecewise functions, always check the boundary conditions (like \( x = -2 \)) to ensure proper continuity and behavior.

The query submitted by the user: function j(x) = x + 1, x ≤ -2; 12x^2 + 3x - 20, x > -2

Explore how to work with the piecewise function j(x), defined by different expressions for values of x ≤ -2 and x > -2. This problem involves key algebraic concepts, including solving quadratic equations and analyzing the behavior of piecewise functions. Ideal for students in Grades 10-12.

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