Elenathehomeschooler
  • Elenathehomeschooler
1. For each of the following functions, (a) describe the domain and range, and (b) sketch the graph. a. f(x) ^5sqr(x-4)+2
Mathematics
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katieb
  • katieb
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Elenathehomeschooler
  • Elenathehomeschooler
@jim_thompson5910 can you help me ring the range and domain?
Elenathehomeschooler
  • Elenathehomeschooler
*find
anonymous
  • anonymous
is it \[f(x)=\sqrt[5]{x-4}+2\]?

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Elenathehomeschooler
  • Elenathehomeschooler
yes
anonymous
  • anonymous
you can take an odd root (3,5,7,...) of ANY number
anonymous
  • anonymous
i.e. the there are no restrictions on the domain
Elenathehomeschooler
  • Elenathehomeschooler
so the domain would be all real numbers?
anonymous
  • anonymous
yes
Elenathehomeschooler
  • Elenathehomeschooler
how do i find the range?
anonymous
  • anonymous
as x gets larger and larger, so does \(\sqrt[5]{x}\) i.e as \(x\to \infty\) your function goes to infinity as well
anonymous
  • anonymous
and as \(x\to -\infty\) so does your function
anonymous
  • anonymous
that is not really an explanation, though, that is just a fact not sure how to explain it in words
anonymous
  • anonymous
and odd root will have this same property
Elenathehomeschooler
  • Elenathehomeschooler
so for range it would be \[\infty,-\]
anonymous
  • anonymous
all real numbers just like the domain
Elenathehomeschooler
  • Elenathehomeschooler
\[(\infty,-\infty)\]
anonymous
  • anonymous
oh no you don't put the \(-\infty\) on the right! it goes on the left
Elenathehomeschooler
  • Elenathehomeschooler
oh okay

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