Find the indicated functional value for the floor function: f(−0.75)
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To find the indicated functional value for the floor function \( f(x) \) at \( x = -0.75 \), we use the definition of the floor function. The floor function, denoted as \( \lfloor x \rfloor \), returns the greatest integer less than or equal to \( x \).

Given \( x = -0.75 \):

\[ \lfloor -0.75 \rfloor \]

The greatest integer less than or equal to \( -0.75 \) is \( -1 \).

Thus,

\[ \lfloor -0.75 \rfloor = -1 \]

So, the functional value \( f(-0.75) = -1 \).

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Here are 8 related questions that expand on this information:

1. What is the value of the floor function at \( f(3.14) \)?
2. How does the floor function behave for positive fractional values?
3. What is the ceiling function, and how is it different from the floor function?
4. Calculate \( f(-2.5) \) using the floor function.
5. How would you graph the floor function for the range \( -2 \leq x \leq 2 \)?
6. Can the floor function ever return a non-integer value?
7. What is the floor function value of \( \sqrt{2} \)?
8. How does the floor function handle irrational numbers?

**Tip:** The floor function is especially useful in programming and algorithm design for rounding down to the nearest integer.

Learn how to find the indicated functional value for the floor function f(x) at x = -0.75 using the definition of the floor function. Understand how the floor function returns the greatest integer less than or equal to x. Suitable for students in Grades 7-9 studying mathematical functions and operations.

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