warm up: factor each completely a)b) c) d). rational expression: fraction of two polynomials (1)...
DESCRIPTION
b) (2) MULTIPLYING and DIVIDING a)c) d)TRANSCRIPT
WARM UP: Factor each completelya) 3692 xx b) xxx 28287 23
c) 8103 24 xx d) 2764 3 x
Rational Expression: Fraction of TWO polynomials(1) SIMPLIFYING
c)baaaba33
22
a))7)(5(6)7)(2(2
5
3
xxxxxx
b)158152
2
2
xxxx
d)1610102
2
2
xxxx
b)244
6782
2
2
xx
xxxx
(2) MULTIPLYING and DIVIDING
a))3(10
)2)(12()2)(43(
)3(44
7
xxxx
xxxx
c))3)(2(
)4(6)2)(3(
)2)(4(2 72
xxxx
xxxxx
d)984
36586
2
2
xx
xxxx
(3) ADDITION and SUBTRACTION
43
)5)(4(72
xxxxx
a) )3)(2(7
)5)(3(
xx
xxxx
b)
1032
1497
22
xxxxc) 71525
141932
22
xx
xxx
xd)
EVALUATING RATIONAL FUNCTIONS1. Substitute x-value into the function2. Evaluate the numerator and denominator separately3. Reduce the resulting fraction
37)(
xxxf
2103)(
2
xxx
xg
)3(f
)2(f
)3(f
)5(g
)0(g
)1(g
#1) #2)
Practice: Evaluating Rational Functions
324)(
xx
xf 152127)( 2
2
xxxxxh#3) #4)
)1(f
)2(f
)2(f
)4(f
)3(h
)2(h
)0(h
)4(g
Number Lines and Rational Equations1) Find All Zero/ Root Values of the numerator and denominator• ZEROS in the numerator = zero in the graph (y-value)• ZEROS in the denominator = undefined in the graph (no y-value)
2) Write all the Zero/Undefined x-values on the number line
3) Between those x-values pick a number to substitute into function to determine if the graph (y-value) will be positive or negative• REASON: Only time we can change from positive to negative value
is when we have a ZERO or UNDEFINED value of the graph
Example:)7)(2()4)(3(
xxxx
Number Lines and Rational Equations[1]
)3)(3()1)(5(
xxxxx
[2]xx
xxx8
10732
23