Question

baseball the total number of games won by the chicago cubs baseball team each season for five consecutive years is given in the below table. determine the domain, range, and continuity of the function that models the number of wins. table: x (year) 2012, 2013, 2014, 2015, 2016; y (wins) 61, 66, 73, 97, 103. options: a) d = {2012, 2013, 2014, 2015, 2016}; r = {61, 66, 73, 97, 103}; continuous b) d = {61, 66, 73, 97, 103}; r = {2012, 2013, 2014, 2015, 2016}; continuous c) d = {2012, 2013, 2014, 2015, 2016}; r = {61, 66, 73, 97, 103}; discrete d) d = {97,103}; r = {2013, 2014, 2015}; continuous

Explanation:

To determine the domain and range of the function modeling the number of wins for the Chicago Cubs baseball team, we analyze the given data:

Step 1: Identify the Domain (D)

The domain consists of the input values, which are the years (2012, 2013, 2014, 2015, 2016). These are distinct, individual years (discrete data, as years are specific points in time, not a continuous interval). So, the domain \( D = \{2012, 2013, 2014, 2015, 2016\} \).

Step 2: Identify the Range (R)

The range consists of the output values, which are the number of wins (61, 66, 73, 97, 103). These are distinct, individual values (discrete data, as the number of wins is a count and cannot be a continuous range between these values). So, the range \( R = \{61, 66, 73, 97, 103\} \).

Now, we match this with the given options:

• Option A: Domain is continuous (incorrect, as years are discrete).
• Option B: Domain is \(\{61, 66, 73, 97, 103\}\) (incorrect, domain is years, not wins).
• Option C: Domain \( D = \{2012, 2013, 2014, 2015, 2016\} \) and Range \( R = \{61, 66, 73, 97, 103\} \) (matches our analysis, and both are discrete).
• Option D: Domain is \(\{97, 103\}\) (incorrect, domain is all years, not a subset of wins).
• Option E: Range is \(\{2013, 2014, 2015\}\) (incorrect, range is wins, not years).

Answer:

C. \( D = \{2012, 2013, 2014, 2015, 2016\} \); \( R = \{61, 66, 73, 97, 103\} \); discrete