Find the domain and range for y=x^2+9.

Wouldn't the domain and range just be all real numbers since nothing else is really given in the equation? How would you enter "all real numbers" in interval notation? Would it include the infinity sign?

domain is all reals, but since x^2 >= 0 for all x,

y >= 9 for all x.
That is the range.

D: (-∞,+∞)
R: [9,∞)

To find the domain and range of the equation y = x^2 + 9, we need to consider the restrictions on the variables x and y.

1. Domain:
The domain represents all possible values that x can take in the equation. Since there are no explicit restrictions mentioned in the equation, the domain of y = x^2 + 9 is all real numbers. In interval notation, we write this as (-∞, +∞) or (-∞, ∞).

2. Range:
The range represents all possible values that y can take in the equation. In this case, we observe that the square term (x^2) is always non-negative because squaring any real number yields a positive or zero result. Additionally, adding a constant term (+9) does not impact whether the output is positive or negative. Therefore, the range of y = x^2 + 9 includes all real numbers greater than or equal to 9, since the minimum value of y is 9. In interval notation, we write this as [9, +∞).

To summarize:
- Domain: (-∞, ∞) or (-∞, +∞)
- Range: [9, +∞)

Note: The use of interval notation does not include the symbol for infinity (∞). Instead, we use parentheses ( ) for open intervals (when infinity is not included) and brackets [ ] for closed intervals (when infinity is included).