or 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: ?
c. To graph the functions on the same coordinate plane for the relevant domain, we will plot points on a graph using the given functions.
For the light-weight class, the function y = |x - 215| is defined for values of x between 200 and 230.
We can plot points on the graph by substituting different values of x into the function and calculating the corresponding values of y. For example, when x = 200, y = |200 - 215| = 15. Similarly, when x = 230, y = |230 - 215| = 15.
So, the points on the graph for the light-weight class are (200, 15) and (230, 15).
For the heavy-weight class, the function y = |x - 240| is defined for values of x between 230 and 250.
Again, we can plot points on the graph by substituting different values of x into the function and calculating the corresponding values of y. For example, when x = 230, y = |230 - 240| = 10. When x = 250, y = |250 - 240| = 10.
So, the points on the graph for the heavy-weight class are (230, 10) and (250, 10).
Now, plot these points on a coordinate plane and connect them with a line. The graph should show two lines, one for the light-weight class and one for the heavy-weight class.
d. Without the domain restrictions, the functions would overlap at the center of each weight class.
For the light-weight class, the center is at 215 pounds. For the heavy-weight class, the center is at 240 pounds. So, without the domain restrictions, the functions would overlap at x = 215 and x = 240 on the graph.