Questions: What are the four ordered pairs Determine the domain

Solution Steps

1. For the function \( f(x) = \frac{6}{x-7} \), identify the values of \( x \) that make the denominator zero to determine the domain.
2. For the function \( v(x) = (x-7)^3 \), calculate the values of \( v(x) \) for four different values of \( x \) to get four ordered pairs.

The function \( f(x) = \frac{6}{x-7} \) has a denominator that becomes zero when \( x = 7 \). Therefore, the domain of \( f(x) \) is all real numbers except \( x = 7 \): \[ \text{Domain of } f(x): \mathbb{R} \setminus \{7\} \]

The function \( v(x) = (x-7)^3 \) is evaluated at four different values of \( x \):

• For \( x = 6 \): \[ v(6) = (6-7)^3 = (-1)^3 = -1 \]
• For \( x = 7 \): \[ v(7) = (7-7)^3 = 0^3 = 0 \]
• For \( x = 8 \): \[ v(8) = (8-7)^3 = 1^3 = 1 \]
• For \( x = 9 \): \[ v(9) = (9-7)^3 = 2^3 = 8 \]

Thus, the four ordered pairs are: \[ (6, -1), (7, 0), (8, 1), (9, 8) \]

Final Answer