How do you find the domain and range of $f(x)=x^2 - 6x - 10$ ?

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Answer 1 · 2015-09-11T11:52:08

Domain: ${x in RR}$
Range: ${f(x) in RR | f(x) >= -19}$

$f(x) = x^2 - 6x - 10$

Domain: ${x in RR}$

Completing the squares:
$f(x) = (x^2 - 6x + 9 - 9 - 10)$
$= (x - 3)^2 - 19$

Minimum value of $f(x)$ is -19. Therefore range:
$f(x) >= -19$

graph{x^2-6x -10 [-5, 10, -25, 10]}

How do you find the domain and range of f(x)=x^2 - 6x - 10f(x)=x^2 - 6x - 10?