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Problem 1: Let \[f(x) = \frac{3x - 7}{x + 1}.\]Find the domain of $f$. Give your answer using interval notation.

 

 

Problem 2:Let $f(x) = 3(x - 6)^2 + 1$. What is the range of $f$? Express your answer with interval notation.

 Mar 2, 2019
 #1
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\(f(x) = \frac{3x - 7}{x + 1}.\)

 

The domain is all values of x that don't make the denominator = 0

Thus x = - 1    is excluded from the domain

 

So....the domain  is    ( - inf, -1) U (-, inf )

 

 

 

\(f(x) = 3(x - 6)^2 + 1\)

 

This is a parbola that opens upward with a vertex of  (6, 1)

 

So....the range is    [ 1, inf )

 

 

cool cool cool

 Mar 2, 2019

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