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: ?
c. To graph the functions on the same coordinate plane, plot the points for the respective domains.
For the light-weight class (200 < x < 230), plot the points (200, 15) and (230, 15).
For the heavy-weight class (230 < x < 250), plot the points (230, 10) and (250, 10).
Connect the points with a line to represent each function.
d. Without the domain restrictions, the functions would overlap at the point (230, 10). This is the intersection of the two weight classes.
c. To graph the functions on the same coordinate plane, we can plot points along the x-axis within the specified domains for each weight class. For the Light-weight class, the domain is 200 < x < 230, and for the Heavy-weight class, the domain is 230 < x < 250.
For the Light-weight class, we can choose x-values of 200, 210, 220, and 230, and plug them into the function y = |x - 215| to find the corresponding y-values. Similarly, for the Heavy-weight class, we can choose x-values of 230, 235, 240, and 250, and plug them into the function y = |x - 240| to find the corresponding y-values.
Once we have the respective x and y-values for each weight class, we can plot the points and connect them to create the graphs of the functions. The graphs of the functions will be V-shaped.
d. Without the domain restrictions, the functions would overlap at the center point of the weight classes. In this case, the overlap would occur at the x-value where x - 215 = x - 240, which can be simplified to 215 = 240. However, this cannot be true since 215 is not equal to 240. Therefore, the functions do not overlap without the domain restrictions.