Question

Given f(x) = 3x^2 − 6x − 13, what is the domain of f(x)?

Answer 1

What is a domain?

A domain is all the possible x values of a function that has corresponding y values.

There are different ways to find the domain of different equations.

• If f(x)=
  `(1)/(x)`, the domain = all x values but 0

• If f(x)=
  `(x)/((x-6)(x+3))`, solve for 0 in the denominator and the domain= all x values but 6, 3
• If f(x)=
  `(x)/(√(3-x) )`, set the denominator as an inequality (3-x>0) and solve for x. The domain= all x values<3

For parabolas however, the domain is all real numbers. Due to the shape of this function all x-values have corresponding y values on the graph.