Pregunta
Decide whether the relation defines \( y \) as a function of \( x \). Give the domain and range. \( y=x^{9} \)
Ask by Harper Goodwin. in the United States
Feb 27,2025
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\( y = x^9 \) defines y as a function of x. The domain is all real numbers, and the range is all real numbers.
Solución
The relation y = x⁹ does define y as a function of x because for every x-value there is exactly one corresponding y-value obtained by raising x to the ninth power.
Domain: All real numbers (–∞, ∞), since x⁹ is defined for every real number x.
Range: All real numbers (–∞, ∞), because as x varies over all real numbers, x⁹ can take any real value (note that the ninth power, being an odd power, preserves the sign of x).
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Simplifique esta solución The Deep Dive
Absolutely, the relation \( y = x^{9} \) defines \( y \) as a function of \( x \). This is because for every input \( x \), there is exactly one output \( y \). In simpler terms, if you pick a number, raise it to the ninth power, and you’ll always get a unique result! Now, let’s talk about the domain and range. The domain of this function is all real numbers \((-∞, ∞)\) since you can input any real number for \( x \). As for the range, since \( x^{9} \) is an odd power, \( y \) can take on all real values as well, which means the range is also \((-∞, ∞)\). Happy graphing!
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