Answer:
Domain (-∞,∞) Or D={x∈R|-∞<x<∞} Range ={y∈R| y≥-1}
Step-by-step explanation:
1) Domain
As the Domain is the set of all valid quantities of x that satisfies the function, and this polynomial function does not have any restriction or discontinuity the Domain is the whole Real Line.
Or D={x∈R|-∞<x<∞}
2) Range or Image
The Range is the opposite part of the Domain, since we here have the values for y after the values for x were plugged it in.
Algebraically
Since we're dealing with quadratic functions we'll need the parameters and the Vertex to define the Range
Parameters:
a=2
b=4
c=-1
Xv =-b/2a Yv=-Δ/4a
2x²+4x-1
(Xv=1,Yv=-1)
In the Range, we are looking for valid correspondent values for y. And as the parameter of a is 2 and 2 >0 we're looking for the minimum point for y.
And as there is no discontinuity over the graph it's y≥-1
Therefore
R={y∈R| y≥-1} or [-1,∞)
