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Given the following function, find the indicated values. Then write the corresponding ordered pairs.

Find [tex]\( h(-1), h(0) \)[/tex], and [tex]\( h(-4) \)[/tex] when [tex]\( h(x) = x^2 + 5x - 3 \)[/tex].

A. [tex]\((-1, 3), (0, 0), (-4, 39)\)[/tex]

B. [tex]\((-1, -7), (0, -3), (-4, -7)\)[/tex]

C. [tex]\((-1, -7), (0, -3), (-4, -1)\)[/tex]

D. [tex]\((-1, 3), (0, -3), (-4, 33)\)[/tex]


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]