Contoh Soal Lanjutan Nilai Mutlak

 $\begin{array}{l}\\ 6.& \text{Perhatikanlah gambar berikut}\end{array}$

$\begin{array}{l}\\ & \text{Persamaan yang sesuai dengan grafik di atas adalah}....\\ & \begin{array}{l}\\ \text{a}.& y=|x-3|\\ \text{b}.& y=-|x-3|\\ \text{c}.& y=|x+3|\\ \text{d}.& y=|x+6|\\ \text{e}.& y=-|x+6|\end{array}\\ \\ & \text{Jawab}:\mathbf{\text{c}}\end{array}$

$\begin{array}{l}\\ 7.& \text{Diketahui suatu fungsi}y=\left|2x\right|\\ & \text{Nilai saat}-2\text{adalah}....\\ & \begin{array}{l}\\ \text{a}.& -4\\ \text{b}.& -2\\ \text{c}.& 0\\ \text{d}.& 2\\ \text{e}.& 4\end{array}\\ \\ & \text{Jawab}:\mathbf{\text{e}}\\ & \begin{array}{rl}y& =\left|2x\right|\\ \text{saat}& x=-2,\text{maka}\\ y& =|2(-2)|\\ & =|-4|\\ & =-(-4)\\ & =4\end{array}\end{array}$

$\begin{array}{l}\\ 8.& \text{Diketahui suatu fungsi}f(x)=|x-2|\\ & \text{Nilai}f(-2)\text{adalah}....\\ & \begin{array}{l}\\ \text{a}.& 0\\ \text{b}.& 2\\ \text{c}.& 4\\ \text{d}.& 6\\ \text{e}.& 8\end{array}\\ \\ & \text{Jawab}:\mathbf{\text{c}}\\ & \begin{array}{rl}f(x)& =|x-2|\\ \text{Nilai}& f(-2)\text{berarti nilai}\\ \text{saat}& x=-2,\text{maka}\\ f(x)& =|x-2|\\ f(-2)& =|-2-2|\\ & =|-4|\\ & =-(-4)\\ & =4\end{array}\end{array}$

$\begin{array}{l}\\ 9.& \text{Diketahui fungsi}f(x)=|2-4x|\\ & \text{Nilai dari}f(1)\text{adalah}....\\ & \begin{array}{l}\\ \text{a}.& -1\\ \text{b}.& 0\\ \text{c}.& 1\\ \text{d}.& 2\\ \text{e}.& 4\end{array}\\ \\ & \text{Jawab}:\mathbf{\text{d}}\\ & \begin{array}{rl}f(x)& =|2-4x|\\ \text{Nilai}& f(1)\text{berarti nilai}\\ \text{saat}& x=1,\text{maka}\\ f(x)& =|2-4x)|\\ f(1)& =|2-4(1)|\\ & =|-2|\\ & =-(-2)\\ & =2\end{array}\end{array}$

$\begin{array}{l}\\ 10.& \text{Nilai}k\text{yang memenuhi}\left|4k\right|=16\text{adalah... .}\\ & \begin{array}{l}\\ \text{a}.& 2\\ \text{b}.& 4\\ \text{c}.& \pm 2\\ \text{d}.& \pm 4\\ \text{e}.& \pm 8\end{array}\\ \\ & \text{Jawab}:\mathbf{\text{d}}\\ & \begin{array}{rl}\left|4k\right|& =16\\ (4k)& =\pm 16\\ k& =\pm {\displaystyle \frac{16}{4}}\\ & =\pm 4\end{array}\end{array}$