Difficulty: Hard

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Compare the zeros of function P and function Q. Which statement about the zeros of the functions is true?

Diagram for question

Rationale

Function Q has the greater zero, which is 5.

The zero of a function is the value of x for which the function equals zero. In this case, the zero of function Q is greater than that of function P, specifically at the value of 5.

A (Function P has the greater zero, which is 9.) YOUR ANSWER

This statement is incorrect because the zero of function P is not 9; rather, it is lower than the zero of function Q. The zero of function P needs to be correctly identified in order to compare it with function Q.

B (Function P has the greater zero, which is 1.) YOUR ANSWER

This option is also incorrect as it inaccurately presents the zero of function P. The zero of function P is not greater than that of function Q and does not align with the values provided in the question.

C (Function Q has the greater zero, which is 5.) CORRECT

This statement accurately identifies that the zero of function Q is 5, which is indeed greater than the zero of function P. This makes it the correct answer, affirming that function Q has a higher zero.

D (Function Q has the greater zero, which is 4.) YOUR ANSWER

While this statement suggests that function Q has the greater zero, it incorrectly identifies the value as 4. In reality, function Q's zero is 5, thus making this statement false.

Conclusion

In comparing the zeros of functions P and Q, it is evident that function Q, with its zero at 5, surpasses that of function P. The other statements either misidentify the zeros or incorrectly assign greater values to function P, underscoring the importance of accurately determining function values for valid comparisons.

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