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What are the domain and range of f(x) =(1/6)^x + 2?

A.domain: x > - 1/6 ; range: y > 0

B.domain: x ; range: y > 2

C.domain: x is a real number; range: y > 2

D.domain: x ; range: y

User Srking
by
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2 Answers

4 votes

Answer:


\large\boxed{C.\ domain:\ \{x\ |\ x\ \text{is a real number}\};\ range:\ \y\ }

Explanation:


f(x)=\left((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((1)/(6)\right)^x+2\bigg]=\lim\limits_(x\to\infty)\left((1)/(6)\right)^x+\lim\limits_(x\to\infty)2=0+2=2\\\\\lim\limits_(x\to-\infty)\bigg[\left((1)/(6)\right)^x+2\bigg]=\lim\limits_(x\to-\infty)\left((1)/(6)\right)^x+\lim\limits_(x\to\infty)2=\infty+2=\infty\\\\\text{The range:}\ y\in(2,\ \infty)\to\y\ \\\\\bold{Look\ at\ the\ picture}

What are the domain and range of f(x) =(1/6)^x + 2? A.domain:  x > - 1/6 ; range-example-1
User AppleLover
by
8.3k points
2 votes

Answer: Option C

domain: x is a real number; range: y

Explanation:

We have the function
f(x) =((1)/(6))^x + 2

Note that f(x) is an exponential function.

By definition the exponential functions of the form
a(b)^x +k have as domain all real numbers and as range y if
a>0,
b>0

Where a is the main coefficient, b is the base and k is the vertical displacement.

In this case
k = 2,
b=(1)/(6),
a=1

Therefore the domain of f(x) is all real numbers and the range of f(x) is

y > 2

User Jonesinator
by
8.1k points

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