Question

1. what is the domain of the function?

a. (xleq3) or (-infty < xleq3) b. (ygeq - 1) or (-1leq y<infty) c. (yleq3) or (-infty < yleq - 3) d. (xgeq - 1) or (-1leq x<infty)

1. which of the following correctly identifies the domain and range of the mapping and is it a function?

a. domain: ({-2,-1,0}) range: ({-2,3,4}), function
b. domain: ({-2,3,4}) range: ({-2,-1,0}), function
c. domain: ({-2,-1,0}) range: ({-2,3,4}), not a function
d. domain: ({-2,3,4}) range: ({-2,-1,0}), not a function

Explanation:

Step1: Recall domain definition

The domain of a function is the set of all possible input - values (x - values for a function y = f(x)).

Step2: Analyze the graph for domain

For the graph in question 15, looking at the x - values covered by the graph, the left - most x - value is at negative infinity and the right - most x - value is 3. So the domain is \(x\leq3\) or \(-\infty

Step3: Recall domain and range for mapping

For a mapping, the domain is the set of all elements in the first set and the range is the set of all elements in the second set that are paired with elements in the first set. A function is a mapping where each element in the domain is paired with exactly one element in the range.

Step4: Identify domain and range for the mapping in question 16

In the mapping of question 16, the elements in the first set are \(-2\), \(3\), and \(4\), so the domain is \(\{-2,3,4\}\). The elements in the second set that are paired are \(-2\), \(-1\), and \(0\), so the range is \(\{-2,-1,0\}\). Also, since each element in the domain is paired with exactly one element in the range, it is a function. So the answer to question 16 is b.

Answer:

1. a. \(x\leq3\) or \(-\infty
2. b. Domain: \(\{-2,3,4\}\), Range: \(\{-2,-1,0\}\), Function