Question

How do you find the domain and range of `5(x - 2) (x + 1)`?

Answer 1

Domain: `(-oo,+oo)` Range: `[-11.25,+oo)`

Explanation:

Let `f(x) = 5(x-2)(x+1)`

`= 5x^2-5x-10`

`f(x)` is defined `forall x in RR ->` Domain: `(-oo,+oo)`

`f(x)` is a quadratic function of the form `ax^2+bx+c`

Since `a>0`, `f(x)` will have a minimum value at `x=(-b)/(2a)`

`(-b)/(2a) = (-(-5))/(2xx5) = 1/2`

`:. f(x)_min = f(1/2)`

`f(x)_min = 5/4 - 5/2 -10 = -5/4 -10 = -45/4`

`= 11.25`

`f(x)` has no finite upper bound.

Hence, Range: `[-11.25, +oo)`

We can visualise the domain and range of `f(x)` from its graph below.

graph{5(x-2)(x+1) [-24.9, 26.43, -14.9, 10.75]}