Question

3. Find the domain of the function f(x)--2logs (x +3) - 2 Was this domain difficult to find? If so, why? If not, why might someone else find it difficult? List the transformations in their correct order, starting with the parent function a) Parent function: b) Frist transformation c) Second transformation d) Third transformation e) Fourth transformation

Answer 1

$-2\log_5(x+3)-2$ is well defined if and only if $x+3>0\Rightarrow x>-3\Rightarrow \text{Domain is: }{\color{Red} (-3,\infty)}$

The domain was slightly more difficult to find as the logarithmic term is another function of

Parent function is: $f(x)=x$

a) First transformation is $f_1(x)=x+3$

2) Second transformation is: $f_2(x)=\log(x)$

3) Third transformation is: $f_3(x)=-2x$

4) Fourth transformation is: $f_4(x)=x-2$

$\blacksquare$

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