Answered

Welcome to Westonci.ca, the ultimate question and answer platform. Get expert answers to your questions quickly and accurately. Get the answers you need quickly and accurately from a dedicated community of experts on our Q&A platform. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.

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 stopping by. We strive to provide the best answers for all your questions. See you again soon. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.