Determine the amplitude, midline, period and y-intercept of f(x)

f(x) = 4 sin 4x - 1

graph them too

Here is the graph of \( f(x) = 4 \sin(4x) - 1 \). The key features highlighted are:

- The **midline** \( y = -1 \) (red dashed line).
- The **amplitude** limits (green dotted lines), which show the maximum \( y = 3 \) and minimum \( y = -5 \) values.
- The **y-intercept** at \( (0, -1) \) (black vertical line).
  
The graph oscillates between the values \( 3 \) and \( -5 \), with a period of \( \frac{\pi}{2} \).

Do you have any questions or need further details?

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Here are 5 related questions for further practice:
1. What is the phase shift of \( f(x) = 4 \sin(4x) - 1 \)?
2. How does the graph of \( f(x) = \sin(x) \) differ from \( f(x) = 4 \sin(4x) - 1 \)?
3. How would you modify the function to shift it up by 3 units?
4. What would the period be if the coefficient inside the sine function were \( 6x \)?
5. How do we find the maximum and minimum values of a trigonometric function?

**Tip**: The period of a trigonometric function tells you how frequently the sine wave repeats. It is inversely related to the coefficient of \( x \).

Determine the amplitude, midline, period and y-intercept of f(x) = 4 sin 4x - 1. Graph them too.

Learn how to find the amplitude, midline, period, and y-intercept of the sine function f(x) = 4 sin 4x - 1. This problem involves key trigonometric concepts such as the amplitude formula, period calculation, and graphing techniques. Suitable for high school students in Grades 10-12.

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