QUESTION 33 What is the range of the function \( f(x)=4 \sin x \) given that \( 0 \leq x \leq 2 \pi \) ?

The function \( f(x) = 4 \sin x \) oscillates between its minimum and maximum values based on the sine function. Since \( \sin x \) achieves values from \(-1\) to \(1\), when multiplied by \(4\), the range of \( f(x) \) becomes \([-4, 4]\). Therefore, as \(x\) varies from \(0\) to \(2\pi\), \( f(x) \) will take on every value between these two bounds. To visualize this, imagine plotting the function: as you move along the x-axis from \(0\) to \(2\pi\), you'll see the graph peaking at \(4\) and dipping down to \(-4\) like a rollercoaster of sine waves. It's an exciting ride! Just remember, no matter where you are in this interval, \( f(x) \) will always stay within that thrilling range from \(-4\) to \(4\).