Question

Given the function , check which one(s) of the properties it has?

1) strictly decreasing
2) increasing
3) decreasing
4) strictly increasing
5) injective
6) surjective
7) none of the above

Answer 1

The function may have any of the given properties 1-7, as there is not enough information provided to determine which ones it has.

Step-by-step explanation:

The function could be any of the given options. Let's look at each property:

1. Strictly decreasing: A function is strictly decreasing if for every pair of numbers x1 and x2 in the domain, if x1 > x2, then f(x1) < f(x2). To determine if the function is strictly decreasing, we need to examine the slope (derivatives) of the function. If the slope is negative throughout the entire domain, then the function is strictly decreasing.
2. Increasing: A function is increasing if for every pair of numbers x1 and x2 in the domain, if x1 < x2, then f(x1) < f(x2). To determine if the function is increasing, we need to examine the slope of the function. If the slope is positive throughout the entire domain, then the function is increasing.
3. Decreasing: A function is decreasing if for every pair of numbers x1 and x2 in the domain, if x1 < x2, then f(x1) > f(x2). To determine if the function is decreasing, we need to examine the slope of the function. If the slope is negative throughout the entire domain, then the function is decreasing.
4. Strictly increasing: A function is strictly increasing if for every pair of numbers x1 and x2 in the domain, if x1 < x2, then f(x1) < f(x2). To determine if the function is strictly increasing, we need to examine the slope of the function. If the slope is positive throughout the entire domain, then the function is strictly increasing.
5. Injective: A function is injective if it maps distinct elements of the domain to distinct elements of the range. This means that each input has a unique output. To determine if the function is injective, we need to check if there are any repeated outputs for different inputs.
6. Surjective: A function is surjective if every element in the range is mapped to by at least one element in the domain. This means that the function covers the entire range. To determine if the function is surjective, we need to check if there are any missing elements in the range.

Based on the given information, we don't have enough details about the function to determine which of these properties it has. Therefore, the answer is none of the above.