Question

Find the domain and range of the function below.

y = 3x2 - 6x + 5
a.
D: all real numbers
R : (22)
D: all real numbers
R: ( 32)
C. D: (
x2)
R: all real numbers
D: all real numbers
R: all real numbers

Answer 1

A.

Explanation:

Answer 2

Domain: All real numbers

Range:

`[2, \infty )`

EXPLANATION

The given function is

`y = 3 {x}^(2) - 6x + 5`

To find the domain and range of the given function, we complete the square.

`y = 3 ({x}^(2) - 2x )+ 5`

`y = 3 ({x}^(2) - 2x + 1) + 3( - 1)+ 5`

`y = 3 ({x - 1)}^(2) - 3+ 5`

`y = 3 ({x - 1)}^(2) + 2`

The vertex is at (1,2).

The given function is a polynomial and all polynomial functions are defined everywhere.

The domain is all real numbers.

The parabola opens upwards and have vertex at (1,2). Hence the minimum y-value is 2.

The range is

`[2, \infty )`