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Letf(x) = \frac{3x - 7}{x + 1}.Find the range of f. Give your answer as an interval. 

Please enter your response in interval notation. Refer to Formatting Tips below for detailed instructions on formatting your response.

Guest Nov 6, 2014

Best Answer 

 #1
avatar+90996 
+5

$$f(x)=\frac{3x-7}{x+1}$$

 

find the range.

I cannot remember doing questions like this so my method may not be the method taught.

I am feeling my way.

You cannot divide by 0 so x+1 cannot =0, x cannot equal -1

This is a  restriction on the domain - not on the range.  

x=-1 will be a vertical asymptote.

Just looking at it I can see it will be a hyperbola.        (it reminds me of  y=1/x)

We need the horizontal asymptote

ok

$$\\f(x)=\frac{3x-7}{x+1}\\\\
f(x)=\frac{3(x+1)-10}{x+1}\\\\
f(x)=\frac{3(x+1)}{x+1}+\frac{-10}{x+1}\\\\
f(x)=3+\frac{-10}{x+1}\\\\
$now $\;\; \frac{-10}{x+1} \;\;$ cannot equal zero $\\\\
so\;\;f(x)\;\;$cannot equal 3$\\\\$$

 

$$$The range of f is $\;\; (-\infty,3),(3,+\infty)\;\;
$I think that is in interval notation$\\\\
$ I think I would normally write is as $\;\;f(x)\in R\;\; where\;\; f(x)\ne3$$

 

Here is the graph (asymptotes are shown)

https://www.desmos.com/calculator/p9jhxdm5ff

Melody  Nov 7, 2014
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1+0 Answers

 #1
avatar+90996 
+5
Best Answer

$$f(x)=\frac{3x-7}{x+1}$$

 

find the range.

I cannot remember doing questions like this so my method may not be the method taught.

I am feeling my way.

You cannot divide by 0 so x+1 cannot =0, x cannot equal -1

This is a  restriction on the domain - not on the range.  

x=-1 will be a vertical asymptote.

Just looking at it I can see it will be a hyperbola.        (it reminds me of  y=1/x)

We need the horizontal asymptote

ok

$$\\f(x)=\frac{3x-7}{x+1}\\\\
f(x)=\frac{3(x+1)-10}{x+1}\\\\
f(x)=\frac{3(x+1)}{x+1}+\frac{-10}{x+1}\\\\
f(x)=3+\frac{-10}{x+1}\\\\
$now $\;\; \frac{-10}{x+1} \;\;$ cannot equal zero $\\\\
so\;\;f(x)\;\;$cannot equal 3$\\\\$$

 

$$$The range of f is $\;\; (-\infty,3),(3,+\infty)\;\;
$I think that is in interval notation$\\\\
$ I think I would normally write is as $\;\;f(x)\in R\;\; where\;\; f(x)\ne3$$

 

Here is the graph (asymptotes are shown)

https://www.desmos.com/calculator/p9jhxdm5ff

Melody  Nov 7, 2014

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