Questions: Determine whether the equation represents y as a function of x. x^2 + y^2 = 81 Yes No Submit Answer Find the function value, if possible. (If an answer is undefined, enter UNDEFINED.) f(x) = sqrt(x+8) + 2 (a) f(-8) (b) f(1) (c) f(x-8) Submit Answer Use the Vertical Line Test to determine whether the graph represents y as a function of x.

Yes, the relation represents y as a function of x.

• Problem: Determine whether the equation \(x^2 + y^2 = 81\) represents y as a function of x.
• Solution: Solve for y in terms of x and check if each x-value corresponds to exactly one y-value.

Equation: \[ x^2 + y^2 = 81 \]

Solving for y: \[ y^2 = 81 - x^2 \] \[ y = \pm \sqrt{81 - x^2} \]

For each x-value, there are two corresponding y-values (positive and negative square roots), so the equation does not represent y as a function of x.

No, the equation does not represent y as a function of x.

• Problem: Find the function value for \( f(x) = \sqrt{x - 8} + 2 \).

(a) \( f(-8) \): \[ f(-8) = \sqrt{-8 - 8} + 2 = \sqrt{-16} + 2 \] The square root of a negative number is undefined in the real number system.

(b) \( f(1) \): \[ f(1) = \sqrt{1 - 8} + 2 = \sqrt{-7} + 2 \] The square root of a negative number is undefined in the real number system.

(c) \( f(x - 8) \): \[ f(x - 8) = \sqrt{(x - 8) - 8} + 2 = \sqrt{x - 16} + 2 \]

(a) Undefined (b) Undefined (c) \( \sqrt{x - 16} + 2 \)