+0

# LetFind the range of . Give your answer as an interval.

0
339
1

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

Guest Nov 6, 2014

#1
+91432
+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
Sort:

#1
+91432
+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

### 6 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details