Determine the X Values That Cause the Function to Be $$f ( x ) = \frac { ( x - 2 ) } { ( 2 x + 1 ) ( x - 3 ) }$$

question 482

Multiple Choice

Determine the x values that cause the function to be (a) zero, (b) undefined, (c) positive, and (d) negative.
- $$f ( x ) = \frac { ( x - 2 ) } { ( 2 x + 1 ) ( x - 3 ) }$$

• A) (a) \( \left\{2,3,-\frac{1}{2}\right\} \) (b) \( \varnothing \), (c) \( \left(-\infty,-\frac{1}{2}\right) \cup(2,3) \), (d) \( \left(-\frac{1}{2}, 2\right) \cup(3, \infty) \)
• B) (a) \( \{3\} \), (b) \( \left\{3,-\frac{1}{2}\right\} \), (c) \( \left(-\infty,-\frac{1}{2}\right) \cup(2,3),(\mathrm{d})\left(-\frac{1}{2}, 2\right) \cup(3, \infty) \)
• C) (a) \( \{2,3\} \), (b) \( \left\{-\frac{1}{2}\right\} \) (c) \( \left\{-\frac{1}{2}, 2\right) \cup(3, \infty),(\mathrm{d})\left(-\infty,-\frac{1}{2}\right) \cup(2,3) \)
• D) (a) \( \{2\} \), (b) \( \left\{3,-\frac{1}{2}\right\} \), (c) \( \left\{-\frac{1}{2}, 2\right) \cup(3, \infty),(d)\left(-\infty,-\frac{1}{2}\right) \cup(2,3) \)

---

Definitions:

Strenuous Life

A concept promoted by Theodore Roosevelt that advocates for rigorous, active efforts in both personal and national life, emphasizing hard work, dedication, and the vigorous exertion of power.

Manila Bay

A natural harbor in the Philippines serving as a significant site for naval battles, notably the Battle of Manila Bay during the Spanish-American War in 1898.

Stimulus Energies

The physical energy, such as light or sound waves, that activate sensory systems and lead to perception.

Neural Activity

refers to the electrical and chemical processes occurring within neurons, supporting brain functions like thought, emotion, and movement.