Answer:
infinite (unbounded) vertical asymptote discontinuity
Explanation:
To determine the type of discontinuity for the given function
f(t) = t^2 + 2t - 8 / t-2, we need to analyze its behavior as t approaches the point where the denominator becomes zero, which is t = 2
Let's break down the steps:
Identify Points of Discontinuity: The function is undefined when the denominator t - 2 becomes zero, which occurs at t = 2
Check the Behavior at the Discontinuity:
- As t approaches 2 from the left (t < 2), the denominator t − 2 becomes negative, and the numerator becomes positive. This means that the function value approaches negative infinity.
- As t approaches 2 from the right (t > 2), the denominator t − 2 becomes positive, and the numerator remains positive. This means that the function value approaches positive infinity.
Based on the behavior of the function as t approaches 2 from both sides, we can conclude that the function has a vertical asymptote at t = 2 and experiences an infinite (unbounded) discontinuity at this point.
The type of discontinuity for the function f(t) = t^2 + 2t - 8 / t-2 is an infinite (unbounded) vertical asymptote discontinuity at t = 2.