Back
Nonlinear Functions and Set Theory
Mathematics, Grade 7
Back
Study Guide
Provides a quick overview of the topic selected!
Flash Cards
Practice and review the topic selected with illustrated flash cards!
Quiz
Assess students’ understanding of the topic selected!
Worksheets
Print illustrated worksheets!
Games
Engage students with interactive games.
Study Guide Nonlinear Functions and Set Theory Mathematics, Grade 7
❮
1
/
4
❯
NONLINEAR
FUNCTIONS
AND
SET
THEORY
•
A
function
can
be
in
the
form
of
y
=
mx
+
b.
This
is
an
equation
of
a
line,
so
it
is
said
to
be
a
linear
function.
•
Nonlinear
functions
are
functions
that
are
not
straight
lines.
Some
examples
of
nonlinear
functions
are
exponential
functions
and
parabolic
functions.
o
An
exponential
function,
y
=
aˆx, is
a
curved
line
that
gets
closer
to
but
does
not
touch
the
x-axis.
o
A
parabolic
function,
y
=
ax²
+
bx
+c,
is
a
U-shaped
line
that
can
either
be
facing
up
or
facing
down.
•
Graphs
can
be
used
to
represent
different
situations,
like
a
drive
on
a
trip
or
a
ball
thrown
into
the
air.
In
these
cases,
it
is
important
to
read
a
graph
correctly.
•
A
graph
can
also
be
used
to
compare
two
rates.
Rates
are
fractions
in
which
the
numerator
and
denominator
have
different
units
of
measure.
o
Rates
of
change
refer
to
a
change
in
the
numerator
over
a
change
in
time.
Rates
of
change
are
often
used
in
calculating
speed,
such
as
miles
per
hour,
feet
per
second,
or
words
per
minute.
•
Set
theory
refers
to
a
collection
of
objects
in
a
set
and
how
it
can
be
displayed
or
manipulated.
o
A
Venn
diagram
displays
data
in
circles
showing
how
much
data
is
in
a
certain
category
and
how
much
data
overlaps
the
categories.
© Copyright NewPath Learning. All Rights Reserved.
Permission
is
granted
for
the
purchaser
to
print
copies
for
non-commercial
educational
purposes
only.
Visit
us
at
www.NewPathLearning.com.
How
to
use
nonlinear
functions
and
set
theory
Nonlinear
functions
need
to
be
recognized
on
a
graph.
The
figures
below
show
the
two
types
of
nonlinear
functions.
Exponential
function
Parabolic
function
y
=
aˆx
y
=
ax²
+
bx
+c
•
The
y
values
for
any
function,
whether
linear
or
nonlinear,
can
be
found
by
plugging
in
the
x
values
and
evaluating
the
function.
•
Graphs
can
be
used
to
represent
many
situations.
o
A
line
that
goes
up
means
an
increase
of
some
sort,
like
an
increase
of
movement,
a
ball
moving
upwards,
or
a
car
driving.
o
A
horizontal
line
means
no
change,
like
a
car
that
is
stopped.
o
A
line
that
goes
down
means
a
decrease
of
some
sort;
like
a
decline
in
speed
or
temperature.
When
a
graph
has
two
lines
that
cross,
it
shows
where
the
two
equations
are
equal.
© Copyright NewPath Learning. All Rights Reserved.
Permission
is
granted
for
the
purchaser
to
print
copies
for
non-commercial
educational
purposes
only.
Visit
us
at
www.NewPathLearning.com.
•
Rates
can
be
used
with
speed.
If
Jon
drove
594
miles
in
11
hours,
his
rate
of
speed
would
be
54
miles
per
hour.
When
comparing
two
objects
with
different
rates
of
speed
such
as
miles
per
hour
and
feet
per
second,
the
rates
can
be
changed
as
follows:
Ex.
x
miles
x
1
hour
x
1
minute
x
5280
feet
=
(x)(5280)
feet
1
hour
60
min.
60
sec.
1
mile
(60)(60)
sec.
In
the
equation,
the
hours,
the
minutes
and
the
miles
cancel
out
to
leave
feet
per
second
with
the
numbers.
So
to
change
2
mph
into
ft
per
second,
the
answer
would
be
(2)(5280)
feet/
(60)(60)
seconds
or
10,560
ft/3,600
seconds
or
2.93
ft/sec.
•
Set
theory
is
helpful
to
display
an
analyze
data.
With
a
Venn
diagram,
the
data
is
displayed
in
circles
showing
how
much
data
is
in
a
certain
category.
The
Venn
diagram
below
shows
how
many
people
like
only
pizza,
only
subs,
or
both.
The
total
number
of
people
asked
is
33.
•
A
set
has
the
notation:
set
A
=
{x
>12}, s
o
for
the
set
of
people
who
like
only
pizza,
the
set
notation
would
be,
set
Only
Pizza
=
{x
=
12}.
Venn
diagrams
also
can
have
more
than
one
circle
to
represent
three
categories.
© Copyright NewPath Learning. All Rights Reserved.
Permission
is
granted
for
the
purchaser
to
print
copies
for
non-commercial
educational
purposes
only.
Visit
us
at
www.NewPathLearning.com.
Try
This!
What
kind
of
function
is
y
=
aˆx?
What
kind
of
function
is
y
=
ax²
+
bx
+
c?
A
graph
of
Joan
riding
her
bike
shows
a
straight
horizontal
line
for
two
hours.
What
could
that
mean?
If
Roberto
can
type
150
words
in
9
minutes,
how
many
words
can
he
type
per
minute?
What
is
12
mph
changed
to
feet
per
second?
Make
a
Venn
diagram
that
shows:
o
people
who
like
only
vegetable
juice-
5
o
people
who
like
only
milk-
10
o
people
who
like
both-
4
© Copyright NewPath Learning. All Rights Reserved.
Permission
is
granted
for
the
purchaser
to
print
copies
for
non-commercial
educational
purposes
only.
Visit
us
at
www.NewPathLearning.com.
© Copyright 2012-2020
NewPath Learning
. All Rights Reserved.
Privacy Notice
*
Terms of Use