Question

What is the domain and range of `h(x)=3x^2+5x-3`??

Answer 1

Domain is `RR`, range is: `[-5 1/12;+oo)`

Explanation:

As `h(x)` is a polynomial, it is defined for all real numbers (its domain is `RR`)

If you look at the graph:
graph{3x^2+5x-3 [-14.24, 14.24, -7.12, 7.13]}

you will see that the range is `[q;+oo)`.

To calculate the coordinates of the vertex `V=(p,q)` you can use the following formulas:

`p=-b/(2a)` `q=-Delta/(4a)`

To calculate `q` you can also substitute the calculated `p` for `x` in the formukla of the function