Question

1. which statement best describes the function?

a the function is onto.
b the function is one - to - one
c the function is onto and one - to - one.
d the function is neither one - to - one nor onto.

1. define a function and provide an example.
2. true or false: the function shown is not discrete because the domain is a finite set.

a true
b false

Explanation:

Step1: Analyze one - to - one property for question 1

Use the horizontal line test. If any horizontal line intersects the graph of the function at most once, the function is one - to - one. The given graph passes the horizontal line test, so it is one - to - one.

Step2: Analyze onto property for question 1

The range of the function is all real numbers (since the graph extends infinitely in both the positive and negative y - directions), so the function is onto as well.

Step3: Define a function for question 2

A function is a relation where each element in the domain is paired with exactly one element in the range. For example, \(f(x)=2x + 1\), where the domain is the set of all real numbers and for every real number \(x\) in the domain, there is a unique real number \(y = 2x+1\) in the range.

Step4: Analyze discreteness for question 3

A discrete function has a domain that is a set of isolated points. Just because the domain is a finite set does not mean it is not discrete. In fact, the given graph with isolated points is a discrete function. So the statement is false.

Answer:

1. C. The function is onto and one - to - one.
2. A function is a relation where each element in the domain is paired with exactly one element in the range. Example: \(f(x)=2x + 1\)
3. B. False