Westonci.ca makes finding answers easy, with a community of experts ready to provide you with the information you seek. Experience the ease of finding accurate answers to your questions from a knowledgeable community of professionals. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.
Sagot :
To solve this problem, we need to evaluate the given function [tex]\( h(x) = x^2 + 5x - 3 \)[/tex] at three specific values of [tex]\( x \)[/tex]: -1, 0, and -4. Then we will create ordered pairs [tex]\((x, h(x))\)[/tex] for each of these values.
Let's begin by calculating each value step-by-step:
1. Finding [tex]\( h(-1) \)[/tex]:
- Substitute [tex]\( x = -1 \)[/tex] into the function [tex]\( h(x) \)[/tex]:
[tex]\[ h(-1) = (-1)^2 + 5(-1) - 3 \][/tex]
- Calculate the value:
[tex]\[ h(-1) = 1 - 5 - 3 = -7 \][/tex]
- So, the ordered pair is [tex]\((-1, -7)\)[/tex].
2. Finding [tex]\( h(0) \)[/tex]:
- Substitute [tex]\( x = 0 \)[/tex] into the function [tex]\( h(x) \)[/tex]:
[tex]\[ h(0) = 0^2 + 5(0) - 3 \][/tex]
- Calculate the value:
[tex]\[ h(0) = 0 + 0 - 3 = -3 \][/tex]
- So, the ordered pair is [tex]\((0, -3)\)[/tex].
3. Finding [tex]\( h(-4) \)[/tex]:
- Substitute [tex]\( x = -4 \)[/tex] into the function [tex]\( h(x) \)[/tex]:
[tex]\[ h(-4) = (-4)^2 + 5(-4) - 3 \][/tex]
- Calculate the value:
[tex]\[ h(-4) = 16 - 20 - 3 = -7 \][/tex]
- So, the ordered pair is [tex]\((-4, -7)\)[/tex].
Summarizing our results, we have:
- [tex]\( h(-1) = -7 \)[/tex]
- [tex]\( h(0) = -3 \)[/tex]
- [tex]\( h(-4) = -7 \)[/tex]
Thus, the corresponding ordered pairs are:
[tex]\[ (-1, -7), (0, -3), (-4, -7) \][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{B. \, (-1, -7), (0, -3), (-4, -7)} \][/tex]
Let's begin by calculating each value step-by-step:
1. Finding [tex]\( h(-1) \)[/tex]:
- Substitute [tex]\( x = -1 \)[/tex] into the function [tex]\( h(x) \)[/tex]:
[tex]\[ h(-1) = (-1)^2 + 5(-1) - 3 \][/tex]
- Calculate the value:
[tex]\[ h(-1) = 1 - 5 - 3 = -7 \][/tex]
- So, the ordered pair is [tex]\((-1, -7)\)[/tex].
2. Finding [tex]\( h(0) \)[/tex]:
- Substitute [tex]\( x = 0 \)[/tex] into the function [tex]\( h(x) \)[/tex]:
[tex]\[ h(0) = 0^2 + 5(0) - 3 \][/tex]
- Calculate the value:
[tex]\[ h(0) = 0 + 0 - 3 = -3 \][/tex]
- So, the ordered pair is [tex]\((0, -3)\)[/tex].
3. Finding [tex]\( h(-4) \)[/tex]:
- Substitute [tex]\( x = -4 \)[/tex] into the function [tex]\( h(x) \)[/tex]:
[tex]\[ h(-4) = (-4)^2 + 5(-4) - 3 \][/tex]
- Calculate the value:
[tex]\[ h(-4) = 16 - 20 - 3 = -7 \][/tex]
- So, the ordered pair is [tex]\((-4, -7)\)[/tex].
Summarizing our results, we have:
- [tex]\( h(-1) = -7 \)[/tex]
- [tex]\( h(0) = -3 \)[/tex]
- [tex]\( h(-4) = -7 \)[/tex]
Thus, the corresponding ordered pairs are:
[tex]\[ (-1, -7), (0, -3), (-4, -7) \][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{B. \, (-1, -7), (0, -3), (-4, -7)} \][/tex]
Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Find reliable answers at Westonci.ca. Visit us again for the latest updates and expert advice.