How do you sketch the graph $g(x)=-x^5-3$ and $f(x)=x^5$ using transformations and state the domain and range of g?

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Answer 1 · 2017-05-25T13:36:02

$g(x) = -f(x) - 3$ Domain and range = $RR$

If you know x^5 is like x^3 but is not like x^1 because it's not a straight line, then

$f(x) = x^5$ Domain and range = $RR$
$(x,y) mapsto (x,-y)$ Reflection on 0y axis.
$(x, -y) mapsto (x, -y - 3)$ Vertical translaction $y := y - 3$

How do you sketch the graph g(x)=-x^5-3g(x)=-x^5-3 and f(x)=x^5f(x)=x^5 using transformations and state the domain and range of g?