Question

Find the domain and range of the function below.

Answer 1

ANSWER

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

$[2, \infty )$

Answer 2

Answer:

A.

Step-by-step explanation: