What is a Function? Quiz

PDF page 56: The notation used to assert that y is a function of x is y = f (x), where f stands for the set of rules that tell us how to go from x to y. We read y = f (x) as “y equals f of x. Of course, we may use other letters (such as g, h, etc. to represent other functions. This notation sometimes causes confusion, for students have become used now to using letters to represent numbers. So it is useful at this time to be clear that, for the first time, we are using a letter ( f ) to represent an action(implementing a set of rules) rather than a number.

PDF page 56: The notation used to assert that y is a function of x is y = f (x), where f stands for the set of rules that tell us how to go from x to y. We read y = f (x) as “y equals f of x. Of course, we may use other letters (such as g, h, etc. to represent other functions. This notation sometimes causes confusion, for students have become used now to using letters to represent numbers. So it is useful at this time to be clear that, for the first time, we are using a letter ( f ) to represent an action(implementing a set of rules) rather than a number.

PDF page 56: Function Concept: Given two variables, x and y, we will say that y is a function of x if there is a set of instructions (which may be expressed as a formula, algorithm or recipe) that determine a specific y for a given x.

PDF page 60: Before proceeding, this is a good place to introduce a little terminology that goes along with the function concept. First, the set of values for which the function is defined is called the domain of the function. The range of the function is the set of values that can appear as the output of the function. Let’s look over the preceding examples to identify the domain and the range of the function.

PDF page 60: Before proceeding, this is a good place to introduce a little terminology that goes along with the function concept. First, the set of values for which the function is defined is called the domain of the function. The range of the function is the set of values that can appear as the output of the function. Let’s look over the preceding examples to identify the domain and the range of the function.

PDF page 55: Examining the table, we notice several things: first of all, it takes the 8:00 bus three hours 15 minutes to make the trip; furthermore, this time is the time every trip takes. Also, the change between any two departure times is the same as the change between any two arrival times. Graphing these data (see Figure

PDF page 55: in fact, a line of slope 1, since any change in departure time results in precisely the same change in arrival time. We conclude that, whenever a bus leaves Salt Lake City, it arrives in Price 3 hours and 15 minutes later. This we call a model for the given data: in this case the model is linear. We use the model to show us immediately when a bus arrives in Price, for any given departure time from Salt Lake City.

PDF page 55: If a new bus, with departure time 6:30 were to be added to the schedule, we schedule it to arrive in Price at 9:45. More generally, if a bus leaves SLC at D o’clock, it should be expected to arrive in Price at D + 3 : 15 o’clock. Letting A represent the arrival time, we arrive at this relationship between D and A: A = D + 3 : 15. We see that this formula tells us that the arrival time is completely determined by the departure time; that is A is a function of D. In such a statement, we consider A and D as variables in the sense that they can have any (time) value, and the relation A = D + 3 : 15 will hold.

PDF page 55: If a new bus, with departure time 6:30 were to be added to the schedule, we schedule it to arrive in Price at 9:45. More generally, if a bus leaves SLC at D o’clock, it should be expected to arrive in Price at D + 3 : 15 o’clock. Letting A represent the arrival time, we arrive at this relationship between D and A: A = D + 3 : 15. We see that this formula tells us that the arrival time is completely determined by the departure time; that is A is a function of D. In such a statement, we consider A and D as variables in the sense that they can have any (time) value, and the relation A = D + 3 : 15 will hold.

PDF page 56: Here, we do not have a rule to give a value of y corresponding to x = 0. We say that the function is not defined for x = 0, or 0 is not in the domain of the function. For this function, x is a positive number, so we often make explicit that we are only interested in the function for positive values of x. For this function, we say that x and y are inversely proportional in the sense that if x is multiplied by any number, the y is divided by that number.

PDF page 56: Here, we do not have a rule to give a value of y corresponding to x = 0. We say that the function is not defined for x = 0, or 0 is not in the domain of the function. For this function, x is a positive number, so we often make explicit that we are only interested in the function for positive values of x. For this function, we say that x and y are inversely proportional in the sense that if x is multiplied by any number, the y is divided by that number.

PDF page 60: x. Since the domain of a functions is the set of values to which we can apply the rules, the domain of this

PDF page 60: function consists of all numbers on the number line.

PDF page 57: - for a linear function we need only find two points on the graph, and connect them with a line.