An Introduction to Functions Chapter 4
 Pg.
234 – 239
 Obj: Learn how to represent mathematical
relationships using graphs.
 Content Standard: Prepares for F.IF.4
 Pg.
240 – 245
 Obj: Learn how to identify and represent
patterns that describe linear functions.
 Content Standards: A.REI.10 and F.IF.4
 Dependent
Variable – changes in response to
another variable
 Independent Variable – the variable that
determines what happens to the other
variable(s)
 Inputs – values of the independent variable
 Outputs – values of the dependent variable
 Function – a relationship that pairs each
input value with exactly one output value
 Linear Function – a function whose graph is a
nonvertical line or part of a nonvertical line
 Pg.
246 – 251
 Obj: Learn how to identify and represent
patterns that describe nonlinear functions.
 Content Standards: A.REI.10, and F.IF.4
 Nonlinear
Function – a function whose graph
is not a line or part of a line
 Pg.
253 – 259
 Obj: Learn how to graph equations that
represent functions.
 Content Standards: F.IF.5, N.Q.1, and
A.REI.10
 Continuous
Graph – a graph that is unbroken
 Discrete Graph – composed of distinct
isolated points
 Graphing a Function Rule



Use a table of values
Input values for x and solve for y
Graph the points and connect
 Pg.
262 – 267
 Obj: Learn how to write equations that
represent functions.
 Content Standards: N.Q.2, A.SSE.1.a, and
A.CED.2
 Pg.
268 – 273
 Obj: Learn how to determine whether a
relation is a function, find domain and range,
and use function notation.
 Content Standards: F.IF.1 and F.IF.2
 Relation
– a pairing of numbers
 Domain – the x values of a function
 Range – the y values of a function
 Vertical Line Test – if any vertical line passes
through more than one point of the graph,
then for some domain value there is more
than one range value. So the relation is not
a function.
 Function Notation – f(x) = -3x + 1
 Pg.
274 – 281
 Obj: Learn how to identify and extend
patterns in sequences and represent
arithmetic sequences using function
notation.
 Content Standards: F.IF.3, A.SSE.1.a,
A.SSE.1.b, F.BF.1.a, F.BF.2, and F.LE.2
 Sequence
- an ordered list of numbers that
often form a pattern
 Term of a Sequence – each number in the list
 Arithmetic Sequence – the difference
between consecutive terms is constant
 Common Difference – the difference between
consecutive terms
 Recursive Formula – a function rule that
relates each term of a sequence after the
first to the ones before it
 Explicit
Formula – a function rule that relates
each term of a sequence to the term number
A(n)  A(1)  (n  1)d


n – term number
d – common difference