Question 708131
If no restrictions are stated, function {{{f(x)}}} exists for all values of {{{x}}} that let you calculate {{{f(x)}}}.
A polynomial, like {{{f(x)=2x^2+5x-7}}} can be calculated for any {{{x}}},
so its domain is all the real numbers.
If you have to write "all the real numbers" in symbols,
you need to know how your teacher prefers to write that.
It could be (-infinity, infinity),
but there are different ways to state the same thing.
 
NOTE 1:
Some functions have a domain that excludes some numbers.
For example {{{g(x)=sqrt(x)}}} does not exist for any negative {{{x}}}
and {{{h(x)=1/x}}} does not exist for {{{x=0}}}.
 
NOTE 2:
Just as the {{{highlight(domain)}}} of {{{f(x)}}} is the set of all possible {{{x}}} values,
the {{{highlight(range)}}} of {{{f(x)}}}  is the set of all possible {{{f(x)}}} values.
The range of {{{f(x)=2x^2+5x-7=2(x-5/4)62-81/8}}} only includes values such that
{{{f(x)>=-81/8}}}