The Implied Domain of a Formula Worksheet with Answer Key

What's on the worksheet

1. Find the implied domain of each function with a root in interval notation.
   g(x) = \sqrt[4]{9 - 3x}h(x) = \sqrt{x^2 + 4}k(x) = \dfrac{x}{\sqrt[4]{x + 5}}m(x) = \sqrt[3]{x - 1} - \dfrac{2}{x + 3}
2. Find the implied domain of each function that mixes roots and fractions.
   f(x) = \dfrac{x + 2}{\sqrt{x} - 3}h(x) = \sqrt{x - 4} + \dfrac{1}{\sqrt{10 - x}}k(x) = \dfrac{\sqrt{x + 1}}{x^2 - 5x}
3. Find the implied domain of a function with a root and a quadratic denominator, and explain a zero that does not matter.
4. Find the constant k that gives the stated domain, then find a value.
5. Find the implied domain of a function and decide which stated domains can be used.
6. Find the error in Mateo's implied domain of a square root of a quadratic.
7. Word problem: the height of Yuna's kite on a 50 m string.