For a livestock competition, the weight classes for hogs are shown in this table.
Classes:
Light: 200-230 (weight range in lbs.)
Heavy: 230-250 (weight range in lbs.)
a. What is the center of each weight class?
A:
Center of Light class: 215 pounds (lb.)
Center of Heavy class: 240 pounds (lb.)
b. Write functions in terms of y for the range of each weight class. Specify the domain for each.
A:
Light-weight class: y = |x - 215|; 200 \< x \< 230
Heavy-weight class: y = | x - 240|; 230 \< x \< 250
c. Graph the functions on the same coordinate plane for the relevant domain.
A: ?
d. Where would the functions overlap without the domain restrictions?
A: ?
To graph the functions for the weight classes, we will plot the points that fall within the specified domains and connect them with a line.
For the light-weight class, the function is y = |x - 215|, where 200 < x < 230. This means that for any value of x within this range, we calculate the difference between x and 215, and then take the absolute value to get y.
Let's calculate a few points for the light class:
- For x = 200: y = |200 - 215| = 15
- For x = 205: y = |205 - 215| = 10
- For x = 210: y = |210 - 215| = 5
- For x = 215: y = |215 - 215| = 0
- For x = 220: y = |220 - 215| = 5
- For x = 225: y = |225 - 215| = 10
- For x = 230: y = |230 - 215| = 15
Plotting these points on a coordinate plane, we get a V-shaped graph for the light class. The line connecting these points will extend beyond the domain restrictions.
For the heavy-weight class, the function is y = |x - 240|, where 230 < x < 250. Again, we calculate the difference between x and 240 and take the absolute value to get y.
Calculating a few points for the heavy class:
- For x = 230: y = |230 - 240| = 10
- For x = 235: y = |235 - 240| = 5
- For x = 240: y = |240 - 240| = 0
- For x = 245: y = |245 - 240| = 5
- For x = 250: y = |250 - 240| = 10
Plotting these points on the same coordinate plane, we get a V-shaped graph for the heavy class. Again, the line connecting these points will extend beyond the domain restrictions.
Without the domain restrictions, the two weight classes would overlap at the center of their ranges. In this case, both functions would have a y-value of 0. However, since the domains are restricted, there is no overlap between the two functions within their specified ranges.