Question

Rewrite each of the following interval expressions in interval notation:• You can use "inf" and "-inf" for ∞o and -0.a. 0≤xb. x < 8c. -4 < xd. 12 xe. x≤ -8

Answer 1

$\begin{gathered} a)\lbrack0,inf) \\ b)(-\imaginaryI nf,8\operatorname{\rbrack} \\ c)(-4,\imaginaryI nf) \\ d)\lbrack12,inf) \\ e)(-\imaginaryI nf,-8\operatorname{\rbrack} \end{gathered}$Explanation

A closed interval is one that includes its endpoints,. An open interval is one that does not include its endpoints

$\begin{gathered} (a,b)\rightarrow open \\ \lbrack a,b\rbrack\Rightarrow closed \end{gathered}$

Step 1

a)

$0\leq x$

this inequlity represent all the values greater or equal than zero , so from zero to positive infinite

$\lbrack0,inf)$

Step 2

b)

$x\leq8$

all the values smaller or equal than 8, so from negative infinite to eighth

$(-inf,8\rbrack$

c)

$-4all the values greater than -4 ( note that -4 is not included, so open interval)[tex](-4,inf)$

d)

$12\leq x$

all the values greater or equalto 12

$\lbrack12,inf)$

e)

$x\leq8$

all the values greater or equal to -8, hence

$(-inf,-8\rbrack$

I hope this helps you