Transcript 1 - Garnet Valley School District

Rational Functions
By: Elena Fayda, Ana Maroto, Madelynn Walker
What is a rational
function?
*A rational function is
when a polynomial is
divided by another
polynomial.
Steps for Solving
1) Write each
expression as a
fraction
5x-25=1+1
3x
3
5x-25=1+ 1
3x
1 1
2) Find the least
common denominator
(LCD) for the entire
equation.
5x-25=1+1
3x
3
LCD: 3x
5x-25=1+ 1
3x
1 1
3) Apply the LCD to
each fraction within
the problem.
*You only have to
multiply the fractions that do
not already have the LCD
5x-25=1+1
5x-25=1+ 1
3x
3
3x
3 1
LCD: 3x
5x-25=1 (x)+1 (3x)
3x
3 (x) 1 (3x)
4)Simplify each
fraction but, DO NOT
REDUCE! Just
multiply the entire
equation by the LCD
(denominator) to
cancel out the
denominator
5x-25=1+1
3x
3
5x-25=1+ 1
3x
3 1
LCD: 3x
5x-25=1 (x)+1 (3x)
(
3x
3 (x) 1 (3x)
(
9
5x-25=1x+3x
3x
3x 3x
5)Rewrite the equation
without the LCD in the
denominator.
5x-25=1x+3x
3x
3x 3x
5x-25=x+3x
(9
5x-25=1x+3x
3x
3x 3x
5x-25=x+3x
5)Solve for the
variable.
5x-25=4x
-5x
-5x
(
(
9
-25=-x
-1 -1
x=25
Steps for Multiplying
and Dividing
1) Factor the
equation.
x+2
3x+12
x+4
x2 -4
(x+2)(x+4)
3(x+4)(x+2)(x-2)
((
9
x+2
3x+12
2) Cross out the same
factors on the top and
bottom.
x+4
x2 -4
(x+2)(x+4)
3(x+4)(x+2)(x-2)
(x+2)(x+4)
3(x+4)(x+2)(x-2)
3) Rewrite the
equation with what is
left.
*Remember if there
are only numbers left
in the denominator,
put a 1 in the
numerator.
x+2
3x+12
x+4
x2 -4
(x+2)(x+4)
3(x+4)(x+2)(x-2)
(x+2)(x+4)
3(x+4)(x+2)(x-2)
1
3(x-2)
*If you are dividing,
then you need to do
the same steps as
above but change the
sign to multiplication
and switch the second
fraction.
(Keep it, Switch it, Flip it)
5x6
x2y
10x2
y
(5x4)
(y)
(y)
(10x2)
x2
2
Steps for Adding and
Subtracting
1)
1) Find a common
denominator leo
3x-4 + 2x-5
x+3 x+3
LCD: x+3
2) Write expression by
adding or subtracting
the numbers leo
3x-4 + 2x-5
x+3 x+3
LCD: x+3
(3x-4) + (2x-5)
x+3
3)Divide numerator by
common denominator
*Simplify by dividing
common factors
(3x-4) + (2x+5)
x+3
5x+1
x+3
Steps for Graphing
1)
Use shifts and
transformations to
graph horizontal
asymptotes.
f(x)= 2
Left 1
Down 3
-3
X+1
2) Make a table of
values choose x
values to the left and
right of the vertical
asymptote *x=0 needs to
be a table value
f(x)= 2
Left 1
Down 3
-3
X+1
x
Y y
-3
--2.6
-2
-3
0
-1
1
-3
2
-1
3) Plot points
On white board...
4) Identify:
● Domain
● Discontinuities
● Holes
● Vertical Asymptotes
● Horizontal
Asymptotes
● x-intercept
● y-intercept
f(x)= 2 - 3
X+1
Domain: All real numbers, x=-1
Discontinuities: x=-1
Holes: None
VA: x=-1
HA: y=-3
X-Int: -⅓
Y-Int: (0,-1)
Practice Problems
2r2-5r
2r2-5r
2r-5
4x6
2x4
5x2+15x = 10
X+3
x2-2x-3
x2+5x+4
4
➗ 5x + 5
12x-12
15x - 15
8r² x 6r³-9r²