Question

How do you find the domain and range of `f(x)=3x^2-5`?

Answer 1

Domain = `RR` = (`-oo, oo`)
Range = `y>=-5`

Explanation:

Domain is the possible x-values that can be put into the equation.
Range is all the possible y-values that can come out of the equation.

All quadratic equations have a domain of all real numbers, because any x-value can be plugged into the equation, and because the parabola extends width wise for infinity.

A domain of all real numbers can be written as `RR` or (`-oo, oo`).

The range of quadratic equations depends on the vertex. To find the vertex of the equation, first put it in standard form (`ax^2 + bx + c`), which it already is. Then use the formula `(-b)/(2a)`.

`(-b)/(2a)` = `(0)/(6)` = `0`

the x-value of the vertex is 0. substitute it back in to get the y-value.

`f(0) = 3(0)^2 - 5 = 0 - 5 = -5`

So the vertex is (0, -5). The range is either `y>=-5" "`or`" "y<=-5`.

Since `a` is positive, the parabola opens upwards. So the range has to be y is greater than or equal to something.

So the range is `y>=-5`.

Domain and range are easier to find when you have the graph of the equation:graph{3x^2 - 5 [-10.59, 9.41, -6.16, 3.84]}