water accounts for about 60% of a person's body weight.
a. write an equation that represents the water y of a person who weights x pounds. identify the independent variable and the dependent variable.
b. make an input-output table for the equation in part (a) use the inputs 100, 120, 140, and 160.
c. find the domain and range of the function represented by the table.
a)
If a person weighs 'x' pounds, then the amount of water in them is 60% of 'x', which is equal to y.
So,
y = 60% of x
=> y = (60/100)*x
= 0.6x
Since in this case y changes according to the changes made in x, y is the dependent variable.
b)
You have the equation:
y = 0.6x
Plus in the given input values for x, what values of y do you obtain?
c) The domain refers to all the 'x' values in your table. The range refers to all the 'y' values.
a. The equation that represents the water content y of a person who weighs x pounds can be written as:
y = 0.6x
In this equation, the independent variable is x (the weight of the person in pounds) and the dependent variable is y (the water content in the person's body in percentage).
b. Here is an input-output table for the equation y = 0.6x, using the inputs 100, 120, 140, and 160:
| x | y |
|------|-------|
| 100 | 60.0 |
| 120 | 72.0 |
| 140 | 84.0 |
| 160 | 96.0 |
c. The domain of the function represented by the table is the set of all possible input values, which in this case is the weight of a person. So, the domain is {100, 120, 140, 160}.
The range of the function represented by the table is the set of all possible output values, which in this case is the water content percentage. So, the range is {60.0, 72.0, 84.0, 96.0}.
a. The equation representing the water content of a person's body weight can be written as:
y = 0.6x
In this equation, the independent variable is x, which represents the weight of the person in pounds. The dependent variable is y, which represents the amount of water in the person's body in pounds.
b. To create an input-output table for the equation y = 0.6x, we can substitute the given inputs (100, 120, 140, and 160) into the equation and find the corresponding outputs.
Input (Weight in pounds) | Output (Water in pounds)
----------------------------------------------------------
100 | 60
120 | 72
140 | 84
160 | 96
c. The domain of the function represents all possible values for the independent variable, which is the weight of the person. In this case, since we are considering weights that are provided (100, 120, 140, and 160), the domain is {100, 120, 140, 160}.
The range of the function represents all possible values for the dependent variable, which is the water content. Looking at the output values in the table (60, 72, 84, and 96), the range is {60, 72, 84, 96}.