Die funksies $f(x) = - an rac{1}{2} x$ en $g(x) = ext{cos}(x + 90^ ext{o})$ vir $-180^ ext{o} ext{ ≤ } x ext{ ≤ } 180^ ext{o}$ word gegee - NSC Mathematics - Question 6 - 2016 - Paper 2

To plot the two functions, first determine their individual characteristics:

1. Function $g(x) = ext{cos}(x + 90^ ext{o})$:

   • This function is a cosine function shifted by $90^ ext{o}$. It behaves like a sine function (i.e., $g(x) = - ext{sin}(x)$).
   • Calculate the intercepts: It intersects the y-axis at $g(0) = 0$ and oscillates between -1 and 1.
   • Identify maximum and minimum values: Maximum at $y = 0$ and minimum at $y = -1$.
   • Key points include turning points at $x = -90^ ext{o}$ and $x = 90^ ext{o}$ with defined curvatures.
   • Asymptotes are not present due to it being a periodic function.

2. Function f(x) = - an rac{1}{2} x:

   • This function has vertical asymptotes where the tangent function is undefined, specifically at $x = ext{odd multiples of } 180^ ext{o}$.
   • Calculate points of intersection with the x-axis where $f(x) = 0$, solving for $x$.
   • Mark turning points and behavior approaching asymptotes to depict the decrease towards negative infinity near the vertical asymptotes.

Graph both functions on the same set of axes clearly indicating their intercepts, turning points, and asymptotes.