Download Functions

Name _______________________________________ Date __________________ Class __________________
Graphs and Functions
Family Letter: Functions
Dear Families,
Vocabulary
Your student will be learning what a function is and how to
graph a function on a coordinate plane.
These are the math
words we are learning:
dependent variable a
variable that represents
the output of a function
domain the set of all
possible input values of
a function
function a rule that
relates two quantities so
that each input value
corresponds to exactly
one output value
independent variable
a variable that
represents the input of a
function
range the set of all
possible output values
of a function
relation a set of
ordered pairs
vertical line test
a method used to
determine whether a
graph is a graph of a
function
A function is an equation that produces only one output
number for each number that is input. In other words, each
value of x substituted into a function will produce a different
y value, or each x-value corresponds to exactly one y-value.
The student will become familiar with relations, or sets of
ordered pairs. He or she will learn how to tell if a relation is a
function. This can be done by examining the sets of ordered
pairs to see if each x-value corresponds to only one y-value.
Graphically, you can see if a relation is a function by using the
vertical line test.
Determine if each relation represents a function.
A
x
y
0
0
1
2
2
4
3
6
Each input x has only one output y.
The relation is a function.
B.
Use the vertical line test. The
vertical line shown intersects the
graph at two points. The relation
is not a function.
Holt McDougal Mathematics
Name _______________________________________ Date __________________ Class __________________
Graphs and Functions
SECTION B Family Letter: Functions continued
Functions can be easily graphed, using the x value as the first
number in a coordinate and the y value for the second
number. Solve the equation for several values of x and graph
all the coordinates to see what the graph of the function looks
like. An example of how to graph a function is below.
Make a table and graph of y  x2  3.
Make a table of inputs and outputs. Use the table to make
a graph.
x
x2  3
y
3
(3)2  3
12
2
(2)2  3
7
1
(1)2  3
4
0
(0)2  3
3
1
(1)2  3
4
2
(2)2  3
7
3
(3)2  3
12
Understanding functions is very important to the student’s
math education. Point out functions in everyday life. Provide
functions for her or him to graph. This kind of practice will
strengthen her or his skills.
Sincerely,
Ms. Galanis and Mrs. Cohen
Holt McDougal Mathematics
Name _______________________________________ Date __________________ Class __________________
Graphs and Functions
SECTION B At-Home Practice: Functions
Determine if each relation represents a function.
1.
2.
3.
x
y
x
y
2
3
0
1
3
5
2
3
4
7
4
5
4
9
6
7
_______________________
________________________
________________________
Make a function table for each function, for x  2, 1, 0, 1, and 2.
4. y  6x  4
5. y 
x
7
2
6. y  2x  5
Graph each function.
7. y 
x
 (2)
3
8. y  4x  3
Answers: 1. no 2. yes 3. yes 4.
6.
7.
x
2
1
0
1
2
y  2x  5
y  2(2)  5
y  2(1)  5
y  2(0)  5
y  2(1)  5
y  2(2)  5
x
2
1
0
1
2
y
1
3
5
7
9
8.
y  6x  4
y  6(2)  4
y  6(1)  4
y  6(0)  4
y  6(1)  4
y  6(2)  4
9. y  5x  5
y
8
2
4
10
16
5.
x
y
x 7
2
y
2
y
2  7
2
8
1
y
1
7
2
7
0
y
0
7
2
7
1
y
1
7
2
6
2
y
2
7
2
6
1
2
1
2
9.
Holt McDougal Mathematics
Name _______________________________________ Date __________________ Class __________________
Graphs and Functions
Family Fun: Sequence and Function Crossword
Down
1. First number in an ordered pair
2. Kind of sequence made by adding
a fixed quantity to each term
3. Set of numbers that form a pattern
7. Tool used to record values of a
function
9. One number in a pattern
11. Equation that produces one output
for each input
13. Inputs and outputs of a function
mapped on a coordinate plane
Across
4. Number sentence in which the
numbers and variables on each side
of the  are equal
5. With 10 Across, name for the quantity
added to each term in an arithmetic
sequence
6. y value in a function table
8. Operation used to find the next
number in an arithmetic sequence
10. See 5 Across
12. x value in a function table
14. Second number in an ordered pair
Answers: 1. x-coordinate 2. arithmetic 3. sequence 4. equation 5. common 6. output 7. table 8. addition 9. term
10. difference 11. function 12. input 13. graph 14. y-coordinate
Holt McDougal Mathematics