3. The function \( m \) is given by \( m(x)=-3 \tan (4 \pi x) \). What is the period of \( m \) ?

The function \( m(x) = -3 \tan(4 \pi x) \) has its period determined by the argument of the tangent function. The standard period of the tangent function \( \tan(x) \) is \( \pi \). When the argument is of the form \( kx \), the period changes to \( \frac{\pi}{|k|} \). Here, with \( k = 4\pi \), the period becomes \( \frac{\pi}{4\pi} = \frac{1}{4} \). So, the period of \( m(x) \) is \( \frac{1}{4} \). Now, this function can exhibit some interesting behavior. Just like a rollercoaster, the tangent function has vertical asymptotes where it approaches infinity, which can create interesting graphs. So as you explore \( m(x) \), keep an eye on those wild curves that appear every \( \frac{1}{4} \) units along the x-axis!