What is the range of the function $f (x) = x^{2} + 3$ $f(x) = x^2 + 3$ if the domain is {-3, 0, 3}?

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Answer 1 · 2018-06-08T17:59:57

range ${3, 12}$ ${3,12}$

If the domain is restricted to ${- 3, 0, 3}$ ${-3, 0, 3}$ then we need to evaluate each term in the domain to find the range:

$f (x) = x^{2} + 3$ $f(x) = x^2 + 3$

$f (- 3) = x^{2} + 3 = {(- 3)}^{2} + 3 = 12$ $f(-3) = x^2 + 3= (-3)^2 + 3=12$

$f (0) = x^{2} + 3 = 0^{2} + 3 = 3$ $f(0) = x^2 + 3= 0^2 + 3=3$

$f (3) = x^{2} + 3 = 3^{2} + 3 = 12$ $f(3) = x^2 + 3= 3^2 + 3=12$

So the range is ${3, 12}$ ${3,12}$

What is the range of the function f(x) = x^2 + 3f(x)=x2+3f(x) = x^2 + 3 if the domain is {-3, 0, 3}?