The function given is \( y = x^2 + 4 \).
Domain: The domain of a function is the set of all possible input values (x-values). For the function \( y = x^2 + 4 \), there are no restrictions on x. Therefore, the domain is:
\[ \text{Domain} = (-\infty, \infty) \]
Range: The range of a function is the set of all possible output values (y-values). The function \( y = x^2 + 4 \) is a parabola that opens upwards, with its vertex at the point \((0, 4)\). Since the minimum value of \( y \) occurs at the vertex, the lowest point of the parabola is \( 4 \), and as \( x \) moves away from \( 0 \) in either direction (both positive and negative), \( y \) increases towards infinity.
So the lowest value of \( y \) is \( 4 \), and \( y \) can take on all values greater than or equal to \( 4\). Therefore, the range is:
\[ \text{Range} = [4, \infty) \]
In summary:
- Domain: \( (-\infty, \infty) \)
- Range: \( [4, \infty) \)
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