Given the functions defined by $f(x) = ext{cos}(x - 45^ ext{o})$ and $g(x) = -2 ext{sin}x$, where $x ext{ } ext{is in } [0^ ext{o}; 360^ ext{o}]$ 5.1 Draw sketch graphs of $f$ and $g$ on the same set of axes provided in the ANSWER BOOK - NSC Technical Mathematics - Question 5 - 2024 - Paper 2

To sketch the graphs of the functions:

1. Graph of f(x):

   • The function $f(x) = ext{cos}(x - 45^ ext{o})$ is a cosine wave shifted to the right by $45^ ext{o}$. Its amplitude is 1 and it oscillates between -1 and 1.
   • The x-intercepts can be found where $f(x) = 0$: $x - 45^ ext{o} = 90^ ext{o} + k imes 360^ ext{o}$ $x = 135^ ext{o} + k imes 360^ ext{o}$ (for $k=0$) $x = 135^ ext{o}$
   • The turning points occur at $x = 45^ ext{o}, 225^ ext{o}$.

2. Graph of g(x):

   • The function $g(x) = -2 ext{sin}x$ has an amplitude of 2. This function is also periodic and oscillates between -2 and 0.
   • The minimum value occurs when $g(x)$ takes the value of -2 which occurs at $x = 270^ ext{o}$.

3. Graphing: Plot both graphs on the same set of axes, with turning points, intercepts, and the y-intercept (for f: $(0, ext{cos}(-45^ ext{o}))$).