Name:
Activity: Functions II
Math 140B - Penn State Date:
Learning Objectives
• Compute a unit conversion.
• Create a function model of a proportional relationship from a verbal description.
• Identify independent and dependent variables from a verbal description of a model.
• Interpret the meaning of data presented using function notation.
• Build a function from a verbal description.
• Determine the units of a parameter in a model.
Definition 1: Proportional Relationship
Suppose there is a relationship between the quantities A and B. We say
that the quantity A is proportional to the quantity B if there is a constant
k such that proportional to x
A = kB.
The notation
AµB
is frequently used to mean A is proportional to B.
y 5 3
not prop
Measured Quantities and Units
A measured quantity has both a number part and units. We will use units extensively. Some examples are shown in the
table below.
quantity number part units dimensions
12 gallons 12 gallons (gal) volume
3.2 seconds 3.2 seconds (s) time
80 kilometers/hours 80 kilometers/hours (km/hr) speed (length/time)
20.1 milligrams/liter 20.1 milligrams/liter (mg/L) density (mass/volume)
Exercise 1.
Use unit conversion to express the quantities 1 million seconds and 1
billion seconds in more familiar terms.
Activity: Functions II
Math 140B - Penn State Date:
Learning Objectives
• Compute a unit conversion.
• Create a function model of a proportional relationship from a verbal description.
• Identify independent and dependent variables from a verbal description of a model.
• Interpret the meaning of data presented using function notation.
• Build a function from a verbal description.
• Determine the units of a parameter in a model.
Definition 1: Proportional Relationship
Suppose there is a relationship between the quantities A and B. We say
that the quantity A is proportional to the quantity B if there is a constant
k such that proportional to x
A = kB.
The notation
AµB
is frequently used to mean A is proportional to B.
y 5 3
not prop
Measured Quantities and Units
A measured quantity has both a number part and units. We will use units extensively. Some examples are shown in the
table below.
quantity number part units dimensions
12 gallons 12 gallons (gal) volume
3.2 seconds 3.2 seconds (s) time
80 kilometers/hours 80 kilometers/hours (km/hr) speed (length/time)
20.1 milligrams/liter 20.1 milligrams/liter (mg/L) density (mass/volume)
Exercise 1.
Use unit conversion to express the quantities 1 million seconds and 1
billion seconds in more familiar terms.
