Naszkicuj wykresy funkcji i podaj ich zbiory wartości

[avleyi]

a. \(f(x) = \frac{|\tg x|}{\tg x}\)

b. \(f(x) = x \cdot \frac{|\cos x|}{\cos x}\), dla \(x\) należącego do \(\langle-2\pi; 2\pi\rangle\)

[Jerry]

b. \(f(x) = x \cdot \frac{|\cos x|}{\cos x}\), dla \(x\) należącego do \(\langle-2\pi; 2\pi\rangle\)

\(y=f(x)=x \cdot \frac{|\cos x|}{\cos x}=\begin{cases}x \cdot \frac{\cos x}{\cos x}&\text{dla}&\cos x>0\\x \cdot \frac{-\cos x}{\cos x}&\text{dla}&\cos x<0\end{cases}\\
y=f(x)=\begin{cases}x &\text{dla}&x\in\langle-2\pi;-{3\pi\over2})\cup (-{\pi\over2};{\pi\over2})\cup({3\pi\over2};2\pi\rangle\\-x&\text{dla}&x\in(-{3\pi\over2};-{\pi\over2})\cup({\pi\over2};{3\pi\over2})\end{cases}\)

Wykres

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[Jerry]

a. \(f(x) = \frac{|\tg x|}{\tg x}\)

\(y=f(x)=\frac{|\tg x|}{\tg x}=\begin{cases}\frac{\tg x}{\tg x}&\text{dla}&&\tg x>0\\\frac{-\tg x}{\tg x}&\text{dla}&&\tg x<0\end{cases}\\
y=f(x)=\begin{cases}1&\text{dla}&&x\in(k\pi;{\pi\over2}+k\pi)\\-1&\text{dla}&&x\in(-{\pi\over2}+k\pi;k\pi)\end{cases}\wedge k\in\zz\)

Wykres

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