1. **State the problem:** Determine which statements about the function $f(x) = -2\sin(x) - 3$ are true. 2. **Recall the general form and properties:** For a function $f(x) = A\sin(Bx + C) + D$: - Amplitude is $|A|$. - Period is $\frac{2\pi}{|B|}$. - Vertical shift is $D$. - Range is $[D - |A|, D + |A|]$. 3. **Identify parameters:** Here, $A = -2$, $B = 1$, $C = 0$, $D = -3$. 4. **Calculate amplitude:** $$\text{Amplitude} = |A| = |-2| = 2$$ 5. **Calculate period:** $$\text{Period} = \frac{2\pi}{|B|} = \frac{2\pi}{1} = 2\pi$$ 6. **Calculate range:** $$\text{Range} = [D - |A|, D + |A|] = [-3 - 2, -3 + 2] = [-5, -1]$$ 7. **Check each statement:** - "The range of the function is the set of real numbers $-2 \leq y \leq 2$." This is false because the range is $[-5, -1]$. - "The graph of the function is the graph of $f(x) = -2\sin(x)$ shifted 3 units up." This is false because the vertical shift is $-3$, which is 3 units down. - "The amplitude of the function is 2." This is true. - "The period of the function is $4\pi$." This is false because the period is $2\pi$. **Final answer:** The only true statement is that the amplitude of the function is 2.