If \( f \) is continuous on \( (-\infty, \infty) \), what can you say about its graph? (Select all that apply.) The graph of \( f \) has a hole. The graph of \( f \) has a jump. The graph of \( f \) has a vertical asymptote. none of these SUBMIT ANSWER

The continuous nature of the function \( f \) on the interval \( (-\infty, \infty) \) means that its graph does not have any breaks, holes, or jumps. As such, it is smooth and connected across its entire domain. This also rules out the possibility of vertical asymptotes since those represent points where a function becomes undefined. Therefore, we can confidently say that the correct answer is "none of these." Continuity is like a smooth, unbroken line—imagine drawing something on a piece of paper without lifting your pencil. If you can do that from left to right without interruptions, then you've got yourself a continuous graph! Fun fact: continuous functions are guaranteed to achieve both maximum and minimum values on any closed interval, thanks to the famous Extreme Value Theorem.