Precalculus Textbook 8th Edition Section 1.3 Exercise 57 Solution
Question:
Set your calculator to DOT mode and graph the greatest integer function y = int(x) in the window [-4.7, 4.7] by [-3.1, 3.1], Then complete the following analysis:
- Domain:
- Range:
- Continuity:
- Increasing and Decreasing Behavior:
- Symmetry:
- Boundedness:
- Local Extrema:
- Horizontal Asymptote:
- Vertical Asymptote:
- End Behavior:
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Solution:
The given function is f(x) = int(x).
Graph of the function is below.
Then complete the following analysis:
- Domain: All Rea Numbers
- Range: All Integers
- Continuity: Discontinuity at Each Integer Value of x
- Increasing and Decreasing Behavior: Constant on Intervals of Form [k, k+1), where k is integer
- Symmetry: None
- Boundedness: Not Bounded
- Local Extrema: Every Non-Integer is Both a Local Minimum and Local Maximum
- Horizontal Asymptote: None
- Vertical Asymptote: None
- End Behavior: When x tends to -Infinity, then f(x) tends to -Infinity and When x tends to +Infinity, then f(x) tends to +Infinity
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