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6- 5- 4- 3- -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 2 -3- -4 -5 -6+ | Write the domain of the function using interval notation.

6- 5- 4- 3- -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 2 -3- -4 -5 -6+ | Write the domain of the function using interval notation.

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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### Understanding Domains of Functions In this example, we are asked to write the domain of the function using interval notation. #### Graph Analysis: 1. **Axes and Grid**: - The graph is plotted on a Cartesian plane with a grid that has intervals marked from -6 to 6 on both the x-axis and y-axis. - Both axes are divided into equal intervals, with the x-axis labeled from -6 to 6 and the y-axis labeled from -6 to 6. 2. **Parabolic Curve**: - A blue parabolic curve is shown that opens downward. - The curve has a broad peak and spans horizontally from x = -1 to x = 3. 3. **Endpoints**: - The curve begins at the point (-1, -2) and ends at the point (3, -2), with both points indicated by solid blue dots. - These solid dots reveal that the values -1 and 3 are included in the domain. #### Interval Notation: The domain of the function is the set of all x-values for which the function is defined. In this case, it includes all x-values between and including -1 and 3. Writing the domain in interval notation: \[ \boxed{[-1, 3]} \] This interval notation denotes that the domain starts at -1 and ends at 3, with both endpoints included.
Transcribed Image Text:### Understanding Domains of Functions In this example, we are asked to write the domain of the function using interval notation. #### Graph Analysis: 1. **Axes and Grid**: - The graph is plotted on a Cartesian plane with a grid that has intervals marked from -6 to 6 on both the x-axis and y-axis. - Both axes are divided into equal intervals, with the x-axis labeled from -6 to 6 and the y-axis labeled from -6 to 6. 2. **Parabolic Curve**: - A blue parabolic curve is shown that opens downward. - The curve has a broad peak and spans horizontally from x = -1 to x = 3. 3. **Endpoints**: - The curve begins at the point (-1, -2) and ends at the point (3, -2), with both points indicated by solid blue dots. - These solid dots reveal that the values -1 and 3 are included in the domain. #### Interval Notation: The domain of the function is the set of all x-values for which the function is defined. In this case, it includes all x-values between and including -1 and 3. Writing the domain in interval notation: \[ \boxed{[-1, 3]} \] This interval notation denotes that the domain starts at -1 and ends at 3, with both endpoints included.
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