Give an example of a function f(x) with a domain of [0, 5] and a range of infinity

One example of a function that has a domain of [0, 5] and a range of infinity is the function:

f(x) = 1 / (5 – x) for x in the interval [0, 5).

Let’s break down why this function fits the criteria:

• Domain: The domain is defined for x values from 0 to 5. However, at x = 5, the function becomes undefined because we cannot divide by zero. Therefore, we express the domain as [0, 5).
• Range: As x approaches 5 from the left (like 4.9, 4.99, etc.), the value of f(x) goes towards infinity. In other words, as x gets closer to 5, the denominator (5 – x) becomes very small, leading the function’s value to increase without bound.

Thus, the function f(x) = 1 / (5 – x) has a domain of [0, 5) and a range that extends to infinity, making it a suitable example.