QUESTION 1 1.1 By completing the table below, draw the graphs of the following evven functions on the same set of axes provided where \( x \in\left[0^{\circ} ; 360^{\circ}\right] \). Label your graphe clearly by shownite the turning points, \( x \)-intercepts and the \( y \)-intereepts. The graphs of a stowld be axes b) \( f(x)=\cos (x) \) and \( g(x)=3 \cos (x) \) and \( h(x)=\cos (3 x) \). \begin{tabular}{|c|c|c|} \hline\( x^{\circ} \) & \( 0^{\circ} \) \\ \hline \( \sin (x) \) \\ \hline \end{tabular}
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Mind Expander
To properly approach functions like \( f(x) = \cos(x) \), \( g(x) = 3\cos(x) \), and \( h(x) = \cos(3x) \), one can visualize their behavior across \( [0^\circ, 360^\circ] \). For instance, \( f(x) \) oscillates between -1 and 1, while \( g(x) \) scales this oscillation to -3 and 3, meaning it stretches vertically. In contrast, \( h(x) \) has a frequency three times greater than \( f(x) \), completing three full cycles in the same interval. To draw the graphs accurately, make sure to mark your axes and encapsulate all important features. Note the turning points: for \( f(x) \) and \( g(x) \), they occur at multiples of \( 90^\circ \). The \( y \)-intercepts for these functions can be found by evaluating them at \( x = 0^\circ \) which gives \( f(0) = 1 \) and \( g(0) = 3 \). For \( h(x) \), the \( y \)-intercept is also 1. Don’t forget to highlight the \( x \)-intercepts too! For a fun twist, while plotting, you could visualize the three functions as waves of different heights and frequencies. Imagine f(x) as your steady beach wave, g(x) as a massive swell perfect for surfing, and h(x) as a fast-paced ripple that would make for quick splashes!
