Question

Rewrite to make it easy to graph using a translation. Describe the graph: 3√(27x-81) - 5

Answer 1

Numbers 27 and 81 have 27 as common factor which is equal to 3^3. Noting that we can put 27 before brackets write it in form 3^3 and that third root and cube will trim.

$\sqrt[3]{27x - 81} - 5=$
$\sqrt[3]{27(x-3)} - 5 =$
$\sqrt[3]{3^3(x-3)} - 5=$
$3 \sqrt[3]{x-3} - 5$

-5 means that graph is shifted 5 to down.
-3 means it is shifted to right by -3
3 and ∛ represent scaling of graph which can be seen and tested once you draw it. It is harder to explain it with words.