Answered

At Westonci.ca, we make it easy for you to get the answers you need from a community of knowledgeable individuals. Our Q&A platform provides quick and trustworthy answers to your questions from experienced professionals in different areas of expertise. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

Which points lie on the graph of the function [tex]\( f(x) = [x] + 2 \)[/tex]? Check all that apply.

A. [tex]\((-5.5, -4)\)[/tex]
B. [tex]\((-3.8, -2)\)[/tex]
C. [tex]\((-1.1, 1)\)[/tex]
D. [tex]\((-0.9, 2)\)[/tex]
E. [tex]\((2.2, 5)\)[/tex]
F. [tex]\((4.7, 6)\)[/tex]

Sagot :

GinnyAnswer
To determine which points lie on the graph of the function [tex]\( f(x) = \lfloor x \rfloor + 2 \)[/tex], we must check each provided point to see if it satisfies the function. Note that [tex]\( \lfloor x \rfloor \)[/tex] denotes the floor function, which returns the greatest integer less than or equal to [tex]\( x \)[/tex]. We'll evaluate the function at each [tex]\( x \)[/tex]-value and compare it to the given [tex]\( y \)[/tex]-value of each point.

1. Point: (-5.5, -4)
- Evaluate [tex]\( f(-5.5) \)[/tex]:
[tex]\[ f(-5.5) = \lfloor -5.5 \rfloor + 2 = -6 + 2 = -4 \][/tex]
- The y-value is [tex]\(-4\)[/tex], which matches the provided point.
- Conclusion: The point (-5.5, -4) lies on the graph.

2. Point: (-3.8, -2)
- Evaluate [tex]\( f(-3.8) \)[/tex]:
[tex]\[ f(-3.8) = \lfloor -3.8 \rfloor + 2 = -4 + 2 = -2 \][/tex]
- The y-value is [tex]\(-2\)[/tex], which matches the provided point.
- Conclusion: The point (-3.8, -2) lies on the graph.

3. Point: (-1.1, 1)
- Evaluate [tex]\( f(-1.1) \)[/tex]:
[tex]\[ f(-1.1) = \lfloor -1.1 \rfloor + 2 = -2 + 2 = 0 \][/tex]
- The y-value is [tex]\(1\)[/tex], which does not match the function value.
- Conclusion: The point (-1.1, 1) does not lie on the graph.

4. Point: (-0.9, 2)
- Evaluate [tex]\( f(-0.9) \)[/tex]:
[tex]\[ f(-0.9) = \lfloor -0.9 \rfloor + 2 = -1 + 2 = 1 \][/tex]
- The y-value is [tex]\(2\)[/tex], which does not match the function value.
- Conclusion: The point (-0.9, 2) does not lie on the graph.

5. Point: (2.2, 5)
- Evaluate [tex]\( f(2.2) \)[/tex]:
[tex]\[ f(2.2) = \lfloor 2.2 \rfloor + 2 = 2 + 2 = 4 \][/tex]
- The y-value is [tex]\(5\)[/tex], which does not match the function value.
- Conclusion: The point (2.2, 5) does not lie on the graph.

6. Point: (4.7, 6)
- Evaluate [tex]\( f(4.7) \)[/tex]:
[tex]\[ f(4.7) = \lfloor 4.7 \rfloor + 2 = 4 + 2 = 6 \][/tex]
- The y-value is [tex]\(6\)[/tex], which matches the provided point.
- Conclusion: The point (4.7, 6) lies on the graph.

Therefore, the points that lie on the graph of [tex]\( f(x) = \lfloor x \rfloor + 2 \)[/tex] are:

- [tex]\((-5.5, -4)\)[/tex]
- [tex]\((-3.8, -2)\)[/tex]
- [tex]\((4.7, 6)\)[/tex]
Thanks for using our platform. We're always here to provide accurate and up-to-date answers to all your queries. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.