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more than 2 weeks ago

The domain and range of f(x)=(x-3)^2+2 is?

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more than 2 weeks ago
The domain of the function f(x) = (x-3)^2 + 2 is all real numbers because there are no restrictions on the input x.

To find the range, we can consider the vertex of the parabola. The vertex of the parabola (x-3)^2 is at (3, 0) because the x-coordinate of the vertex is the opposite of the constant term in the equation (x-3)^2 and the y-coordinate is 0.

Since the parabola opens upwards, the minimum value of the function occurs at the vertex. Therefore, the range of f(x) is all real numbers greater than or equal to 0.

In interval notation, the range is [0, ∞).
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