Gegee: $f(x) = an x$ en $g(x) = ext{cos}(x - 45^ ext{o})$ vir $x ext{ in } [0^ ext{o}; 360^ ext{o}]$
5.1 Teken sketsgrafieke van $f$ en $g$ op dieselfde assestelsel op die rooster wat in die ANTWOORDEBOEK verskaf is - NSC Technical Mathematics - Question 5 - 2021 - Paper 1
Question 5
Gegee: $f(x) = an x$ en $g(x) = ext{cos}(x - 45^ ext{o})$ vir $x ext{ in } [0^ ext{o}; 360^ ext{o}]$
5.1 Teken sketsgrafieke van $f$ en $g$ op dieselfde asseste... show full transcript
Worked Solution & Example Answer:Gegee: $f(x) = an x$ en $g(x) = ext{cos}(x - 45^ ext{o})$ vir $x ext{ in } [0^ ext{o}; 360^ ext{o}]$
5.1 Teken sketsgrafieke van $f$ en $g$ op dieselfde assestelsel op die rooster wat in die ANTWOORDEBOEK verskaf is - NSC Technical Mathematics - Question 5 - 2021 - Paper 1
Step 1
5.1 Teken sketsgrafieke van $f$ en $g$
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Answer
In this step, sketch the graphs of the functions f(x)=anx and g(x)=extcos(x−45exto) in the specified range. Ensure to plot key points, turning points, and asymptotes. For f, the function has vertical asymptotes at 90exto and 270exto, while for g, identify its x-intercepts and turning points. Make sure to label the axes clearly and include all important characteristics of both graphs.
Step 2
5.2.1 $f$ ongedefinieerd is
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Answer
The function f(x)=anx is undefined at points where it has vertical asymptotes. Thus, for x=90exto and x=270exto, f(x) is undefined.
Step 3
5.2.2 $f(x) imes g(x)
eq 0$ waar $x ext{ in } [90^ ext{o}; 180^ ext{o}]$
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Answer
In the interval [90exto;180exto], f(x) is undefined at 90exto and g(x) is non-zero at other points within the interval except for its x-intercepts. Thus, the value of x such that f(x)imesg(x)eq0 would occur when 90exto<x<135exto or x=180exto.
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