- A recipe book shows measurement conversions for tablespoons to cups. It shows that 8 tablespoons converts to 0.5 cup and 24 tablespoons converts to 1.5 cups.
- Which function is undefined for x = 0? y = RootIndex 3 StartRoot x minus 2 EndRoot y = StartRoot x minus 2 EndRoot y = RootIndex 3 StartRoot x + 2 EndRoot y = StartRoot x + 2 EndRoot
The correct answer and explanation is:
Correct Answer:
The function y=x−2y = \sqrt{x – 2} is undefined for x=0x = 0.
Explanation (300 words):
To determine which function is undefined at x=0x = 0, let’s analyze each of the given functions:
- y=x−23y = \sqrt[3]{x – 2}:
This represents the cube root of x−2x – 2. The cube root function is defined for all real numbers because the cube root of a negative number is still a real number (e.g., −83=−2\sqrt[3]{-8} = -2). Substituting x=0x = 0, we get y=−23y = \sqrt[3]{-2}, which is valid. So, this function is defined at x=0x = 0. - y=x−2y = \sqrt{x – 2}:
This represents the square root of x−2x – 2. The square root function is only defined for non-negative numbers because the square root of a negative number is not a real number. Substituting x=0x = 0, we get y=−2y = \sqrt{-2}, which is undefined in the real number system. Therefore, this function is undefined at x=0x = 0. - y=x+23y = \sqrt[3]{x + 2}:
Similar to the first function, this is a cube root function. Substituting x=0x = 0, we get y=23y = \sqrt[3]{2}, which is defined. Hence, this function is defined at x=0x = 0. - y=x+2y = \sqrt{x + 2}:
This represents the square root of x+2x + 2. Substituting x=0x = 0, we get y=2y = \sqrt{2}, which is defined because 2 is non-negative. Hence, this function is defined at x=0x = 0.
Conclusion:
The square root function y=x−2y = \sqrt{x – 2} is undefined for x=0x = 0 because it involves taking the square root of a negative number (−2-2), which is not real.