https://file.aiquickdraw.com/mathbot/file/1727666061306e8o319ma.jpg

The function given in the image is:

\[
f(x) = -6 |3x - 2| + 10
\]

This is an **absolute value function** because it involves the absolute value of a linear expression \( |3x - 2| \).

Absolute value functions typically have a "V"-shaped graph and are piecewise defined, reflecting across the x-axis. The transformation details are as follows:
- The coefficient \(-6\) in front of the absolute value stretches the graph vertically and reflects it downwards.
- The \(|3x - 2|\) causes a horizontal shift.
- The \(+10\) shifts the graph vertically upward by 10 units.

Therefore, the correct answer is **Absolute Value**.

Would you like further clarification or details? Here are some related questions:

1. How do you graph absolute value functions?
2. What is the effect of the coefficient in front of the absolute value term?
3. How do vertical and horizontal shifts affect absolute value functions?
4. Can an absolute value function ever be quadratic?
5. How does the piecewise definition of absolute value work?

**Tip:** The absolute value function can be thought of as a combination of two linear functions, one for when the expression inside is positive, and one for when it's negative.

What type of function is f(x)? f(x) = -6 |3x - 2| + 10

Understand the absolute value function f(x) = -6|3x - 2| + 10. This problem covers key algebraic concepts such as transformations of absolute value functions, including vertical stretching, reflection, and horizontal and vertical shifts. Suitable for high school students in Grades 9-12.

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