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: ?
Answer this Question
To graph the functions for the weight classes, we will plot the points on the coordinate plane using the relevant domain and range.
For the light-weight class, the function is y = |x - 215|, where x represents the weight of the hog. In this case, the domain is 200 < x < 230, as the weight range for the light class is from 200 to 230 pounds.
To graph this function, you can choose different values for x within the given range, substitute them into the equation, and calculate the corresponding y values. Plot these points on a graph and connect them with a smooth curve. Repeat this process for a few more values of x to get a better representation of the function.
For the heavy-weight class, the function is y = |x - 240|, where x represents the weight of the hog. In this case, the domain is 230 < x < 250, as the weight range for the heavy class is from 230 to 250 pounds.
Again, choose different values for x within the given range, substitute them into the equation, and calculate the corresponding y values. Plot these points on the same graph used for the light-weight class and connect them with a smooth curve.
By graphing both functions on the same coordinate plane, you will be able to see where they overlap. Without the domain restrictions, the overlapping region would represent the weight range that belongs to both the light and heavy classes. However, as the domain restrictions limit the weight ranges for each class, the overlapping region may be limited or non-existent.
To determine the overlapping region without the domain restrictions, you could find the intersection points of the two functions by setting them equal to each other and solving for x. The resulting x-values would represent the weights at which the hogs would fall into both weight classes.