Please only answer Q113 ### Trigonometric Graph AnalysisIn Exercises 113–116, determine whether each statement is true or false. (A and B are positive real numbers.)**113.** The graph of $ y = -A \cos(Bx) $ is the graph of $ y = A \cos(Bx) $ reflected about the x-axis. **114.** The graph of $ y = A \sin(-Bx) $ is the graph of $ y = A \sin(Bx) $ reflected about the x-axis.**115.** The graph of $ y = -A \cos(-Bx) $ is the graph of $ y = A \cos(Bx) $.**116.** The graph of $ y = -A \sin(-Bx) $ is the graph of $ y = A \sin(Bx) $.### ExplanationFor each of the given functions, we need to determine if the described transformation (reflection, etc.) is correctly stated.1. **Exercise 113:** - $ y = -A \cos(Bx) $ versus $ y = A \cos(Bx) $: - The negative sign outside the cosine function reflects the graph vertically (about the x-axis). The statement is **true**.2. **Exercise 114:** - $ y = A \sin(-Bx) $ versus $ y = A \sin(Bx) $: - The sine function $ \sin(-Bx) $ is equivalent to $ -\sin(Bx) $. This would actually reflect the graph horizontally (about the y-axis), not the x-axis. Hence, **false**.3. **Exercise 115:** - $ y = -A \cos(-Bx) $ versus $ y = A \cos(Bx) $: - The cosine function $ \cos(-Bx) $ is equivalent to $ \cos(Bx) $, as cosine is an even function. The negative sign outside the cosine function reflects the graph vertically, which matches the original. Therefore, it's **true**.4. **Exercise 116:** - $ y = -A \sin(-Bx) $ versus $ y = A \sin(Bx) $: - Since $\sin(-Bx) = -\sin(Bx)$ and there is a negative sign outside, the two negatives

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Description: Please only answer Q113 ### Trigonometric Graph AnalysisIn Exercises 113–116, determine whether each statement is true or false. (A and B are positive real numbers.)**113.** The graph of $ y = -A \cos(Bx) $ is the graph of $ y = A \cos(Bx) $ refl

The reflection of the point (x,y) about the x-axis is (x,-y). Let be the equation of the graph of…

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In Exercises 113-116, determine whether each statement is true or false. (A and B are positive real numbers.) 115. The graph of y = -A cos(-Bx) is the graph of y = A cos(Bx). 116. The graph of y = -A sin(-Bx) is the graph of y = A sin(Bx). 113. The graph of y = -A cos(Bx) is the graph of A cos(Bx) %3D reflected about the x-axis. A sin(-Bx) is the graph of y = A sin(Bx) 114. The graph of y = reflected about the x-axis.

In Exercises 113-116, determine whether each statement is true or false. (A and B are positive real numbers.) 115. The graph of y = -A cos(-Bx) is the graph of y = A cos(Bx). 116. The graph of y = -A sin(-Bx) is the graph of y = A sin(Bx). 113. The graph of y = -A cos(Bx) is the graph of A cos(Bx) %3D reflected about the x-axis. A sin(-Bx) is the graph of y = A sin(Bx) 114. The graph of y = reflected about the x-axis.

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Please only answer Q113

### Trigonometric Graph Analysis

In Exercises 113–116, determine whether each statement is true or false. (A and B are positive real numbers.)

**113.** The graph of $ y = -A \cos(Bx) $ is the graph of $ y = A \cos(Bx) $ reflected about the x-axis.

**114.** The graph of $ y = A \sin(-Bx) $ is the graph of $ y = A \sin(Bx) $ reflected about the x-axis.

**115.** The graph of $ y = -A \cos(-Bx) $ is the graph of $ y = A \cos(Bx) $.

**116.** The graph of $ y = -A \sin(-Bx) $ is the graph of $ y = A \sin(Bx) $.

### Explanation

For each of the given functions, we need to determine if the described transformation (reflection, etc.) is correctly stated.

1. **Exercise 113:**
- $ y = -A \cos(Bx) $ versus $ y = A \cos(Bx) $:
- The negative sign outside the cosine function reflects the graph vertically (about the x-axis). The statement is **true**.

2. **Exercise 114:**
- $ y = A \sin(-Bx) $ versus $ y = A \sin(Bx) $:
- The sine function $ \sin(-Bx) $ is equivalent to $ -\sin(Bx) $. This would actually reflect the graph horizontally (about the y-axis), not the x-axis. Hence, **false**.

3. **Exercise 115:**
- $ y = -A \cos(-Bx) $ versus $ y = A \cos(Bx) $:
- The cosine function $ \cos(-Bx) $ is equivalent to $ \cos(Bx) $, as cosine is an even function. The negative sign outside the cosine function reflects the graph vertically, which matches the original. Therefore, it's **true**.

4. **Exercise 116:**
- $ y = -A \sin(-Bx) $ versus $ y = A \sin(Bx) $:
- Since $\sin(-Bx) = -\sin(Bx)$ and there is a negative sign outside, the two negatives

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