GM The Domain, Range, Intercepts, Zeroes

The Domain, Range,
Intercepts, Zeroes, and

Asymptotes of
Rational Functions
General Mathematics
Objectives: 1. determine the intercepts,
At the end of the zeroes, and asymptotes of
lesson, you must be rational functions; and
able to:
2. find the domain and range of a
rational function.
3/1/20XX SAMPLE FOOTER TEXT 2

The 3 Saddest Love Stories (with a Bonus Happy Ending)
Math tells us three of the saddest love

stories:
1. The Tragic Tangent Line
Meaning, some people are
Tangent line is "a line that touches
only meant to meet one
a curve at a point without crossing
another at one point in their
over" lives but are forever parted.
Math tells us three of the saddest love

stories:
2. The Awful Asymptote
An asymptote isMeaning,
"a line thatthere are people
a curve
approaches, aswho may get closer
it heads and
towards
infinity" closer to one another but
will never be together.
Math tells us three of the saddest

You may encounter love
stories: potential people, bump
3. The Painful Parallel
onto them, see them from
Parallel lines "lie afar,
on the same
but willplane
neverand are
actually
the same distanceget apart
to over
know and meet their
entire length." them; even in the longest
time.
Bonus Love Story:

(The Patient) Perpendicular Lines
Perpendicular lines are intersecting lines
that form right angles (90near future,
In the degrees).
you'll
also meet someone, at
the right place and at
the right time.
Love Can Be as Easy as

1, 2, & 3
Love and Math, when
separated, pose a
difficulty.
Love in Math, however,
can bring probability.
Domain, Range, Intercepts, Zeroes, Asymptotes
The domain of a function

is the set of all values
that the variable x can
take.
The range of a function is

the set of all values that
f(x) can take.
The y-intercept is the

function value when x = 0.
An asymptote is "a line that a curve

approaches, as it heads towards
infinity“.
Even though the curve approaches
the line, it will never touch the line.
Asymptotes can be used to

determine the domain and range of
rational functions.
An asymptote for a function f(x) is a
straight line which is approached but
never reached by f(x).
Rational functions exhibit three

types of asymptotes:
1. Vertical Asymptote
2. Horizontal Asymptote
3. Oblique Asymptote
Vertical asymptote.
The vertical line x = a is a vertical
asymptote of a function f if the graph
of f either increases or decreases
without bound as the x-values
approach a from the right or left.
Finding the Vertical Asymptotes of a Rational
Function
1. Reduce the rational function to lowest terms by
cancelling out the common factor/s in the
numerator and denominator.
2. Find the values a that will make the denominator
of the reduced rational function equal to zero.
3. The line x = a is a vertical asymptote.


Oblique Asymptote. An asymptote which is
slanted is an oblique asymptote.
An oblique asymptote is an asymptote of the
form y = ax + b with a non-zero.
Rational functions have oblique asymptotes
if the degree of the numerator is one more
than the degree of the denominator.
Find the zeroes, intercepts, asymptotes,
domain, and range of the following rational
functions.


Zero/es: -2/7
Equate all of the factors in the
numerator to 0
7x + 2 = 0 ….. 7x = -2 ….. x = -2/7



You may just cover or remove all

terms with x in the given rational
function.






To get the range,

replace f(x) by y and
solve for x in terms

of y.

The graph of a rational function is a smooth
curve.
The graph passes through all the points on
the x-axis except on x = 1/7. Therefore, the
Horizontal Asymptote: y = 1/3 domain is the set of all real numbers except
1/7.
The graph passes through all the points on
the y-axis except on y = 1/3. Therefore, the
range is the set of all real numbers except
1/3.
x-intercept: (-2/7, 0)
Vertical Asymptote: x = 1/7
y-intercept: (0, -2/3)

Find the zeroes, intercepts, asymptotes,
domain, and range of the following rational
functions.




To get the oblique asymptote, compute for the

quotient of the numerator and denominator of the
given rational function using either long method of
division or the synthetic division.

-3 1 8 -20
-3 -15
1 5 -35
x-intercept: (-10, 0)
x-intercept: (2, 0)
Vertical Asymptote: x = -3
y-intercept: (0, -20/3)
Oblique Asymptote: y = x + 5
Thank
you!

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The Domain, Range,

Intercepts, Zeroes, and

3/1/20XX SAMPLE FOOTER TEXT 2

Math tells us three of the saddest love

Math tells us three of the saddest love

Math tells us three of the saddest

Bonus Love Story:

Love Can Be as Easy as

The domain of a function

The range of a function is

The y-intercept is the

An asymptote is "a line that a curve

Asymptotes can be used to

Rational functions exhibit three

You may just cover or remove all

y-intercept: (0, -2/3)

To get the oblique asymptote, compute for the

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