Question

y=-2x²-8x-5 domain and range

Answer 1

Answer:

Domain: All real numbers

Range: y≤3

Step-by-step explanation:

The given function is

$y = - 2 {x}^{2} - 8x - 5$

This is a polynomial function.

The domain is set of all values of x, that makes this function defined.

Since polynomial functions are defined everywhere, the domain is all real numbers.

To find the range we put the function in vertex form:

$y = - 2( {x}^{2} + 4x) - 5$

$y = - 2( {x}^{2} + 4x + 4) - 5 + - 4 \times - 2$

$y = - 2( {x} + 2)^{2} - 5 + 8$

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

The maximum value is 3

The function turns downward, hence the range is:

$y \leqslant 3$