How do you find the domain and range for #F(x) = x^2 - 3#?

1 Answer
Gió
Jul 1, 2015

Domain: all real #x#;
Range: #y>=-3#

Explanation:

Your function is a Quadratic, and can be represented graphically by a Parabola.
Your function can accept any value of #x# so that the domain will be all the Real #x#.

The range is a little bit tricky...!

Your function has a minimum value (the vertex of your parabola) whose #y# value gives an idea of the range (it is the lowest point attained by your function).

The coordinates of the vertex can be found as:
#x_v=-b/(2a)=0#
#y_v=-Delta/(4a)=-(b^2-4ac)/(4a)=-3#
Where your equation #x^2-3# is in the form #ax^2+bx+c# with:
#a=1#
#b=0#
#c=-3#
So the range (the possible #y# values of your function) will be all the values #y>=-3#

Graphically:
graph{x^2-3 [-8.89, 8.89, -4.444, 4.445]}

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