Question 6 (Bonus) (2 points) Given $$ y=-3 \cos (4 x-2)+10 $$. What is the shift? (round to 2 decimal places.)

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To determine the shift of the function $$ y = -3 \cos(4x - 2) + 10 $$, we need to analyze the components of the cosine function.

The general form of a cosine function is given by:

$$
y = A \cos(B(x - C)) + D
$$

where:
- $$ A $$ is the amplitude,
- $$ B $$ affects the period,
- $$ C $$ is the horizontal shift,
- $$ D $$ is the vertical shift.

In the given function $$ y = -3 \cos(4x - 2) + 10 $$:

1. **Identify the vertical shift $$ D $$**:
   - The vertical shift is $$ D = 10 $$.

2. **Identify the horizontal shift**:
   - We can rewrite the argument of the cosine function to identify the horizontal shift:
   $$
   4x - 2 = 4(x - \frac{1}{2})
   $$
   This shows that the function is shifted horizontally by $$ \frac{1}{2} $$ units to the right.

Thus, the horizontal shift $$ C $$ is $$ \frac{1}{2} $$.

3. **Final answer**:
   - The shift is $$ 0.50 $$ (rounded to two decimal places).

Therefore, the shift is $$ \boxed{0.50} $$.
The shift is 0.50.

Question 6 (Bonus) (2 points)
Given . What is the shift? (round to 2 decimal places.)

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Question 6 (Bonus) (2 points) Given . What is the shift? (round to 2 decimal places.)