How do you find the domain and the range of the function #f(x)= x^2 - 2x -3#?

1 Answer
Mar 26, 2018

Answer:

Domain: #(-oo, oo)# Range: #[-4, oo)#

Explanation:

In general, the domain, or #x# values which yield an output #f(x),# of a polynomial function is all real numbers, denoted by #(-oo, oo)# in interval notation.

Range becomes more specific. This is a quadratic function. In general, the range, or #y-#values for which the function exists, of a quadratic with vertex at #(h,k)# is #[k, oo)#, OR #(-oo, k]# if the parabola is inverted (it isn't in this case -- we don't begin with #-x^2#).

So, let's find the vertex.

We have #f(x)=ax^2+bx+c=x^2-2x-3, a=1, b=-2, c=-3#

#h=-b/(2a)=2/2=1#

#k=f(h)=f(1)=1-2-3=-4#

The range is then #[-4, oo]#