Mathematics, 28.06.2019 06:30 DM3449
What are the domain and range of f(x) =(1/6)^x + 2? a. domain: {x | x > - 1/6} ; range: {y | y > 0} b. domain: {x | x > 1/6} ; range: {y | y > 2} c. domain: {x | x is a real number}; range: {y | y > 2} d. domain: {x | x is a real number}; range: {y | y > โ2}
Answers: 2
![f(x)=\left(\dfrac{1}{6}\right)^x+2\\\\\text{The domain:}\ x\in\mathbb{R}\to\{x\ |\ x\ \text{is a real number\}}\\\\\lim\limits_{x\to\infty}\bigg[\left(\dfrac{1}{6}\right)^x+2\bigg]=\lim\limits_{x\to\infty}\left(\dfrac{1}{6}\right)^x+\lim\limits_{x\to\infty}2=0+2=2\\\\\lim\limits_{x\to-\infty}\bigg[\left(\dfrac{1}{6}\right)^x+2\bigg]=\lim\limits_{x\to-\infty}\left(\dfrac{1}{6}\right)^x+\lim\limits_{x\to\infty}2=\infty+2=\infty\\\\\text{The range:}\ y\in(2,\ \infty)\to\{y\ |\ y2\}\\\\\bold{Look\ at\ the\ picture}](/tpl/images/0026/1757/e1471.png)
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What are the domain and range of f(x) =(1/6)^x + 2? a. domain: {x | x > - 1/6} ; range: {y |...
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