CCII
Functions and Function Notation Day 2
Name _________________________________#______
Domain and Range: For any function f(x), it is customary to refer to the variable x as the input and the
function value f(x) as the output. Many functions are only defined for some input values. Those numbers
make up what is called the domain of the function. Similarly, only some numbers will occur as outputs of
the function. Those numbers make up what is called the range of the function.
There are two ways to think about domain and range for a function that models a real-world situation.
On one hand, you might ask what numbers are realistic or practical as inputs and outputs. On the other
hand, you might ask what numbers theoretically can be used as inputs for a given function rule and what
numbers will result as outputs (regardless of whether they make sense in the specific situation.
(1) Consider again the function rule 𝐼(𝑑) =
8
𝑑2
relating sound intensity and distance from a speaker.
(a) Which variable represents inputs? _________________ Which variable represents outputs? ________________
(b) Give an example of a number that theoretically cannot be used as an input to the rule. ______________
Give an example of a number that cannot possibly be an output from the rule. _________________
(c) Evaluate each of the following, if possible.
I(-1) = ______________
I(-2) = _________________
I(0) = ____________________
I(-10) = ______________
(d) Find the values of d that will satisfy the following equations, if possible.
I(d) = 8 _______________
I(d) = -0.5 _______________
I(d) = 0 _______________
I(d) = 32 _____________
(e) What are the theoretical domain and range of the function I(d)? In other words, what values of d can
be used as inputs to the rule for I(d) and what range of output values will occur over that domain?
Theoretical Domain: ___________________________________
Theoretical Range: __________________________________
(f) Look at a take and graph of the function I(d) on your calculator. Explain how the table and graph
match the theoretical domain and range listed in part (e).
(g) When I(d) is used as a model of the relationship between sound intensity and distance from a source,
what might seem to be practical limits on the domain and range of the function?
Practical Domain: ______________________________________
Practical Range: _____________________________________
Check Your Understanding
The graph to the right shows the height of a
basketball from a player’s free throw attempt on its
path to the basket that is 15 feet from the foul line.
(a) Explain why the height of the ball is a function
of distance from the foul line.
(b) Explain why the distance from the foul line is
not a function of height of the ball.
(c) If h(x) gives the height in feet of the ball when it is above a spot x feet from the foul line:
(i) What information is expressed by h(5) = 14?
(ii) What value of y satisfies the equation y = h(10)? ___________ What does that fact tell you about the
flight of the player’s shot?
(iii) What value(s) of x satisfy the equation 10 = h(x)? What do the value(s) tell about the flight of the
player’s shot?
(iv) What are the practical domain and range of the function as shown on the graph?
Practical Domain: ______________________________
Practical Range: ___________________________________________
(v) What kind of function would best model the relationship shown on the graph? _________________________
(vi) What would be the theoretical domain and range of such a function?
Theoretical Domain: ___________________________________
Theoretical Range: __________________________________