Contoh Soal Lanjutan Nilai Mutlak

 $\begin{array}{ll}\\ 6.&\textrm{Perhatikanlah gambar berikut}\\ \end{array}$

$\begin{array}{ll}\\ &\textrm{Persamaan yang sesuai dengan grafik di atas adalah}\: ....\\ &\begin{array}{llll}\\ \textrm{a}.&y=\left | x-3 \right |\\ \textrm{b}.&y=-\left | x-3 \right |\\ \color{red}\textrm{c}.&y=\left | x+3 \right |\\ \textrm{d}.&y=\left | x+6 \right |\\ \textrm{e}.&y=-\left | x+6 \right |\\ \end{array}\\\\ &\textrm{Jawab}:\quad \color{red}\textbf{c}\\ \end{array}$

$\begin{array}{l}\\ 7.&\textrm{Diketahui suatu fungsi}\: \: y=\left | 2x \right |\\ &\textrm{Nilai saat}\: \: -2\: \: \textrm{adalah}\: ....\\ &\begin{array}{llll}\\ \textrm{a}.&-4\\ \textrm{b}.&-2\\ \textrm{c}.&0\\ \textrm{d}.&2\\ \color{red}\textrm{e}.&4\\ \end{array}\\\\ &\textrm{Jawab}:\quad \color{red}\textbf{e}\\ &\color{blue}\begin{aligned}y&=\left | 2x \right |\\ \textrm{saat}&\: \: x=-2,\: \: \textrm{maka}\\ y&=\left | 2(-2) \right |\\ &=\left | -4 \right |\\ &=-(-4)\\ &=4 \end{aligned} \end{array}$

$\begin{array}{l}\\ 8.&\textrm{Diketahui suatu fungsi}\: \: f(x)=\left | x-2 \right |\\ &\textrm{Nilai}\: \: f(-2)\: \: \textrm{adalah}\: ....\\ &\begin{array}{llll}\\ \textrm{a}.&0\\ \textrm{b}.&2\\ \color{red}\textrm{c}.&4\\ \textrm{d}.&6\\ \textrm{e}.&8\\ \end{array}\\\\ &\textrm{Jawab}:\quad \color{red}\textbf{c}\\ &\color{blue}\begin{aligned}f(x)&=\left | x-2 \right |\\ \textrm{Nilai}&\: \: f(-2)\: \: \textrm{berarti nilai}\\ \textrm{saat}&\: \: x=-2,\: \: \textrm{maka}\\ f(x)&=\left | x-2 \right |\\ f(-2)&=\left | -2-2 \right |\\ &=\left | -4 \right |\\ &=-(-4)\\ &=4 \end{aligned} \end{array}$

$\begin{array}{l}\\ 9.&\textrm{Diketahui fungsi}\: \: f(x)=\left | 2-4x\right |\\ &\textrm{Nilai dari}\: \: f(1)\: \: \textrm{adalah}\: ....\\ &\begin{array}{llll}\\ \textrm{a}.&-1\\ \textrm{b}.&0\\ \textrm{c}.&1\\ \color{red}\textrm{d}.&2\\ \textrm{e}.&4\\ \end{array}\\\\ &\textrm{Jawab}:\quad \color{red}\textbf{d}\\ &\color{blue}\begin{aligned}f(x)&=\left | 2-4x \right |\\ \textrm{Nilai}&\: \: f(1)\: \: \textrm{berarti nilai}\\ \textrm{saat}&\: \: x=1,\: \: \textrm{maka}\\ f(x)&=\left | 2-4x) \right |\\ f(1)&=\left | 2-4(1) \right |\\ &=\left | -2 \right |\\ &=-(-2)\\ &=2 \end{aligned} \end{array}$

$\begin{array}{l}\\ 10.&\textrm{Nilai}\: \: k\: \: \textrm{yang memenuhi}\: \: \left | 4k \right |=16\: \: \textrm{adalah... .}\\ &\begin{array}{llll}\\ \textrm{a}.&2\\ \textrm{b}.&4\\ \textrm{c}.&\pm 2\\ \color{red}\textrm{d}.&\pm 4\\ \textrm{e}.&\pm 8 \end{array}\\\\ &\textrm{Jawab}:\quad \color{red}\textbf{d}\\ &\color{blue}\begin{aligned}\left | 4k \right |&=16\\ (4k)&=\pm 16\\ k&=\pm \displaystyle \frac{16}{4}\\ &=\pm 4 \end{aligned}\end{array}$