Absolutely! One great example of a function that meets your criteria is the function:
f(x) = 1 / (5 – x)
Let’s break this down to understand its domain and range:
- Domain: The function f(x) is defined for all values of x in the interval [0, 5). The function approaches infinity as x approaches 5, but it never actually reaches 5 (this is why we use a parenthesis instead of a bracket, indicating that 5 is not included in the domain).
- Range: As x approaches 5, the denominator (5 – x) gets smaller and smaller, pushing the value of f(x) towards infinity. Conversely, if we look at the other end of the interval: when x = 0, f(0) equals 1/5, which is a finite number. Hence, the output values of f(x) can start from 1/5 and extend towards positive infinity.
So, the function f(x) = 1 / (5 – x) has a domain of [0, 5) and a range of (1/5, ∞). This means that as x moves within the specified domain, the outcome will continue rising towards infinity, fulfilling your requirements!