Question

Consider the equation y = (x + 2). Write a conjecture about the relationship between the zero and the value of the power of the exponent when a equals 1, an even number, or an odd number. Justify your answer.

A) When a = 1, the zero of the equation occurs at x = -2. For even values of a, the zero occurs at x = -2 + 2k, where k is an integer. For odd values of a, the zero occurs at x = -2 + 2k, where k is an integer.
B) When a = 1, the zero of the equation occurs at x = -2. For even values of a, the zero occurs at x = -2 - 2k, where k is an integer. For odd values of a, the zero occurs at x = -2 + 2k, where k is an integer.
C) When a = 1, the zero of the equation occurs at x = -2. For even values of a, the zero occurs at x = -2 + 2k, where k is an integer. For odd values of a, the zero occurs at x = -2 - 2k, where k is an integer.
D) When a = 1, the zero of the equation occurs at x = -2. For even values of a, the zero occurs at x = -2 - 2k, where k is an integer. For odd values of a, the zero occurs at x = -2 - 2k, where k is an integer.

Answer 1

The relationship between the zero and the value of the power of the exponent when a equals 1, an even number, or an odd number can be expressed through a conjecture with justification.

Step-by-step explanation:

The conjecture about the relationship between the zero and the value of the power of the exponent when a equals 1, an even number, or an odd number is:

When a = 1, the zero of the equation occurs at x = -2.

For even values of a, the zero occurs at x = -2 + 2k, where k is an integer.

For odd values of a, the zero occurs at x = -2 - 2k, where k is an integer.

The justification for this conjecture is based on analyzing the equation and observing the patterns of the zeros for different values of a.