Respuesta :
f(x) has the range of [-12 to ∞].
Domain and range
The domain is the value of x and the range is the value of y.
Given
f(x) = x² + 6x -3 is a function of varaible x.
To find
The range of this f(x).
How to find the range of the f(x)?
f(x) is the equation o parabola.
let's find the vertex of the parabola.
In f(x) add and subtract 9. then
f(x) = x² + 6x + 9 -9 -3
f(x) = (x² + 2×3x + 9) -9 -3
f(x) = ( x +3 )² -12
Hence the vertex of the parabola is on 12 units downward in -y-direction and it is an upward parabola so it will go up to ∞ in +y direction.
Thus, f(x) has the range of [-12 to ∞].
More about the domain and range link is given below.
https://brainly.com/question/12208715
