LESSON
6.1
Identifying and Representing
Functions
How can you identify and represent functions?
Texas Essential
Knowledge and Skills
The student is expected to:
Proportionality—8.5.G
Identify functions using sets of ordered pairs, tables, mappings, and graphs.
Mathematical Processes
8.1.E
Create and use representations to organize, record, and communicate mathematical
ideas.
ADDITIONAL EXAMPLE 1
Determine whether each relationship is a
function.
A.
function
B.
not a function
ADDITIONAL EXAMPLE 2
Determine whether each relationship is a
function.
A.
not a function
B.
function
ADDITIONAL EXAMPLE 3
The graph shows the relationship between the
width of a sticker and the length of the sticker
sold at an art store. Is the relationship
represented by the graph a function? Explain
why.
Yes; for each x-value, there is only one y-value.
6.1 LESSON QUIZ
8.5.G
1. There are 12 iron-on patches in 4 packages. Each
package has the same number of patches. Write
a rule in words for the number of packages Leah
needs to buy to get x patches. Then write the
rule as an algebraic expression.
Divide the number of patches by 3;
Determine whether each relationship is a
function.
2.
function
3.
not a function
Determine whether each relationship is a
function.
4. The graph shows the relationship between the
number of texts a person sends and the number
of hours the person spends outside during the
summer. Is the relationship represented by the
graph a function? Explain.
No; at least one of the input
values is paired with more than
one output value; in fact, many
of the input values are paired
with more than one output value.
The inverse of a relationship is found by switching
the coordinates in each ordered pair of the
relationship. So, for each ordered pair (x, y) in the
relationship, the ordered pair (y, x) will appear in
its inverse. Graph the function {(1, 3), (2, 4), (3,
5), (–1, 1), (–3, –1)}, find its inverse, and graph
the inverse. Is the inverse of this function a
function? Try to find a counterexample to
determine whether the inverse of a function is
always a function.
Inverse of the function: {(3, 1), (4, 2), (5, 3), (1, 1),
(–3, –1)}; yes, the inverse of the function is a
function. Sample answer (counterexample):
function: {(5, 2),
(7, 2), (–3, 1), (–5, 0)}; inverse of the function:
{(2, 5), (2, 7), (1, –3), (0, –5)}; the inverse is not
a function. So, the inverse of a function is not
always a function.
How can you identify and represent functions?
Sample answer:
Some ways to represent a function are a mapping
diagram, a table, a graph, and ordered pairs. To
determine whether a relationship is a function,
check that each input value is matched with only
one output value.