The function \( f(x) = -6 \) is a constant function. This means that no matter what value of \( x \) you plug into the function, the output will always be \(-6\).

### Key Points:
1. The graph of this function would be a horizontal line at \( y = -6 \) on the coordinate plane.
2. The domain of the function is all real numbers, \( (-\infty, \infty) \), since you can input any \( x \)-value.
3. The range of the function is just the single value \( \{-6\} \) because the output is always \(-6\), regardless of \( x \).
4. The function does not have any slope, as it's a constant line, so the slope is \( 0 \).
5. This function does not have any roots (zeros), as it never crosses the \( x \)-axis.

Would you like to see more details or have any questions on this?

### Related Questions:
1. What is the graphical interpretation of a constant function like \( f(x) = -6 \)?
2. How do you find the domain and range of constant functions?
3. Can a constant function like this ever have an inverse function?
4. How does a constant function differ from a linear function with a non-zero slope?
5. What happens to the graph if the constant changes from \( -6 \) to another number, say \( 3 \)?

**Tip:** A constant function has the same output value for any input. This makes its graph a flat horizontal line!

Explore the concept of constant functions with a focus on f(x) = -6. Learn how to graph this function, understand its domain and range, and recognize that it represents a horizontal line on the coordinate plane. Ideal for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation