Question

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

Answer 1

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.

Answer 2

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

Answer 3

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

Answer 4

yes

Answer 5

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.

Answer 6

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

Answer 7

for domain and range?

Answer 8

yes

Answer 9

[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

Answer 10

and for infinity we always use commas

Answer 11

ok thanks so much!