is there a step by step solution to help find the range and domain of a function besides graphing in the calculator? f(x)= x^3-9x+6

the domain is easy: you just have to check for which values of x the function has no meaning. So for example denominator cannot be 0 or under square root you cannot have negative.

For the range you need to check the function. x^3-9x+6 the dominant part of a polynomial is always the highest power, so x^3 here

Do you know how does this function look like? f(x)=x^3

yes

OK. So this function will be nearly like that, and x^3 goes from - infinity to +infinity, so this function also will do the same.

ok thanks. How do yu know when to use brackets [] or commas()?

for domain and range?

yes

[a,b] means all the numbers between a and b including a and b (a,b) means all the numbers between a and b excluding a and b

and for infinity we always use commas

ok thanks so much!