Question: B. Tujuan Kegiatan \nMelalui kegiatan ini peserta didik mampu menentukan domain suatu fungsi dan \nmenyajikannya dalam bentuk garis bilangan dengan tepat.\n\nC. Kegiatan \nTentukan domain dari fungsi berikut, kemudian gambarkan hasilnya pada garis bilangan.\n\nh(x) = \sqrt{x + 9}\n\nDiskusikan bersama kelompokmu: \n1. Tentukan domain fungsi. \n2. Jelaskan mengapa ada nilai tertentu yang tidak boleh menjadi anggota domain. \n3. Gambarkan domain fungsi tersebut pada garis bilangan.\n\nLangsung jawaban \nx + 9 \geq 0 \nx \geq -9
1. **Stating the problem:** We need to find the domain of the function $$h(x) = \sqrt{x + 9}$$ and represent it on a number line.
2. **Formula and rules:** The square root function $$\sqrt{y}$$ is defined only when $$y \geq 0$$ because the square root of a negative number is not a real number.
3. **Apply the rule to the function:** For $$h(x) = \sqrt{x + 9}$$, the expression inside the square root must be non-negative:
$$x + 9 \geq 0$$
4. **Solve the inequality:**
$$x + 9 \geq 0$$
$$x \geq -9$$
5. **Explain why some values are excluded:**
Values of $$x$$ less than $$-9$$ make $$x + 9$$ negative, which is not allowed under the square root for real numbers. Therefore, those values are not in the domain.
6. **Domain in interval notation:**
$$[-9, \infty)$$
7. **Graphical representation:**
On the number line, the domain is all points from $$-9$$ to positive infinity, including $$-9$$ itself (closed point) and shading to the right.
**Final answer:** The domain of $$h(x) = \sqrt{x + 9}$$ is $$x \geq -9$$ or $$[-9, \infty)$$.