Question

The domain of f(x) = 2x 2 + 4x - 1 is . The range of f(x) = 2x 2 + 4x - 1 is

Answer 1

Answer:

The domain (-∞,∞) and the range (-∞,∞)

Step-by-step explanation:

Answer 2

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,∞)