Math  /  Geometry

QuestionExercise Sketch the graphs of the following, inserting relevant values. 1. f(x)=40<x<5f(x)=05<x<8f(x)=f(x+8).\begin{array}{ll} f(x)=4 & 0<x<5 \\ f(x)=0 & 5<x<8 \\ f(x)=f(x+8) . & \end{array} 4. f(x)=x20<x<πf(x)=πx2π<x<2πf(x)=f(x+2π)\begin{aligned} f(x) & =\frac{x}{2} \quad 0<x<\pi \\ f(x) & =\pi-\frac{x}{2} \quad \pi<x<2 \pi \\ f(x) & =f(x+2 \pi) \end{aligned}  2. f(x)=3xx20<x<3f(x)=f(x+3).\text { 2. } \begin{aligned} f(x) & =3 x-x^{2} \quad 0<x<3 \\ f(x) & =f(x+3) . \end{aligned} 3. f(x)=2sinx0<x<πf(x)=0π<x<2πf(x)=f(x+2π).\begin{array}{ll} f(x)=2 \sin x & 0<x<\pi \\ f(x)=0 & \pi<x<2 \pi \\ f(x)=f(x+2 \pi) . \end{array} 5. f(x)=x240<x<4f(x)=44<x<6f(x)=06<x<8\begin{array}{ll} f(x)=\frac{x^{2}}{4} & 0<x<4 \\ f(x)=4 & 4<x<6 \\ f(x)=0 & 6<x<8 \end{array} f(x)=f(x+8).f(x)=f(x+8) .

Studdy Solution
The solution consists of the five graphs sketched as described in the steps above.
Each graph shows the different pieces of the function within one period, and the repeating nature of the function is understood.

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