Question

for parts a and b answer the following questions.
a. in a science experiment, the amount of water displaced in a graduated cylinder is a function of the number of marbles placed in the cylinder. the results of the experiment are recorded in the following table.
number of marbles, n 1 2 3 4 5
volume of water displaced, v (ml) 20 40 60 80 100
b. forensic anthropologists predict the height of a male based on the length of his femur. the following table demonstrates this functional relationship.
length of femur, l (inches) 8 10 12 14 16
height, h (inches) 43 47 51 55 59
a. plot the ordered pairs. choose the correct graph below.
a. graph not included in text
b. graph not included in text
c. graph not included in text
d. graph not included in text
determine if a continuous or discrete graph is more appropriate for the situation. choose the correct answer below.
a. since a fraction of a marble does not make sense in this situation, this is a discrete function.
b. since the volume of water displaced can have fractional values, this is a continuous function.

Explanation:

Step1: Analyze the nature of marbles

The number of marbles can only be whole - numbers. A fraction of a marble has no physical meaning in this context.

Step2: Recall the definition of discrete and continuous functions

A discrete function has distinct, separate values for the independent variable. A continuous function can take on any value within an interval for the independent variable.

Answer:

A. Since a fraction of a marble does not make sense in this situation, this is a discrete function.