Question

Given `f(x) = 2x^2 - 3`, what is its domain, range and y-intercept?

Answer 1

Domain: `(-oo, oo)`
Range: `[-3,oo)`
y-intercept : `(0,-3)`

Explanation:

Domain of `f(x)` is the set of points where `f(x)` is defined.
So, `f(x)=2x^2-3` is defined for all real values of x,
hence domain is given by `(-oo,oo)`.

The minimum value of `f(x)` is at x=0
`f(0)=2(0)^2-3=-3`
The maximum value of function is at `oo`
so range is `[-3.oo)`.

the function intercepts at y-axis at a point where x=0,
so `f(0)=-3`
ie `(x,y)=(0,-3)`.