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Drop That Bubble!!!
Guess the missing
then drop that bubble!
© 2006 Doug Clarke
Commutative Property
Which Property?
3a+4=4+3a
movement
Associative Property
Which Property?
(2a+5)+3=2a+(5+3)
( ) changed
Additive Identity
Which Property?
10x+0 = 10x
Multiplicative Identity
Which Property?
(20X)1 = 20x
Additive Inverse
-50a+50a = 0
Which Property?
Multiplicative Inverse
(1/5) (5) = 1
Which Property?
Reflexive Property
Which Property?
3x+2 = 3x+2
Symmetric Property
Which Property?
If 5+5=10, then 10 = 5+5
(If, then)(2 =)
Distributive Property
Which Property?
5 (a+4) = 5a +20
Transitive Property
Which Property?
If 4 = 2a and 2a = 5p, then 4=5p
(If, then 3 =)
Linear Function
Type of Function?
Equation has no exponents or symbols.
Y= 3x +5
Substitution Property
Which Property?
If (5 + x) = Z and x = 2 then (5+2) =z
Commutative Property
Of
Multiplication
Which Property?
(3+2x)5=5(3+2x)
Multiplication Property
Of Equality
Which Property?
If (x + 6) = 2 then 3(x+6) = 3(2)
Quadratic
Parabola
Function?
The equation has an exponent of 2.
Y = 3x^2 - 6
Absolute Value
Function?
The equation has bars.
Y = / 2x + 3/
Cubic Function
Function?
3 Directions.
Y = x^3+2
Exponential Function
Function?
The equation has an exponent that is
a letter. (Hockey stick)
Y = 3^x
Roots, Zeros, Solutions
X-intercepts
All where the graph intersects the x-axis
(4 answers)
Factors
Roots, x-intercepts, zeros, & solutions are
Opposites of ___________.
Write the equation for: If y varies
Directly as x.
Y= kx
Write the equation for: If y varies
As as y.
Y = k/x
Write the equation for: If y varies directly
As x and inversely as z.
Y= kx/z
Formula for joint variation
y/xy
Has a pattern of addition:
Arithmetic Series and
Sequence
Proportion for Direct Variation
1st x / 2nd x = 1st y/2nd y
Has a pattern of multiplication:
Geometric Series and
Sequence
Solutions for one graph are where?
Where the graph touches the x axis.
Where they touch each
other
Solutions for more than one graph are
Where?
Stat Edit Y=
Plot 1 Zoom 9 Stat Calc
What are the steps for finding the
Line or curve of Best Fit?
100%
Area under the curve is what %?
68%
Within 1 standard deviation is what %?
95%
Within 2 standard deviations is what %?
99.7%
Within 3 standard deviations is
What %?
(lower, upper,mean,s.d.)
To calculate % in an interval
With normalcdf:
Mean is 0
S.D is 1
When calculating a probability with
A z-score the mean is ____and the
Standard deviation is ____
Permutation
Order matters (Math PRB #2)
Combination
Order does not matter
(PRB #3)
GCF
When factoring
Polynomials, look
For the ____ 1st.
(5x+2)(5x-2)
Factor:
25x^2 - 4
(3y-1)
(9y^2+3y+1)
Factor:
27y^3-1
(5x+4)
(25x^2-20x+16)
Factor:
125x^3+64
Factor:
49x^2-25
(7x+5)(7x-5)
Imaginary
Numbers are also
…
Complex
numbers
< or > have
___ circles.
Open
When do graphs
Have closed
Circles?
Equal signs
=
Solve by
Factoring:
X^2-2x-15=0
X=5
X=-3
Solve using the
Quadratic
Formula:
2x^2+4x-3=0
(-2+ or- square
Root of 10)/2
3x^2-7x=-10
Has how many
And what type of
solutions?
2 imaginary or
2 complex
Describe f(x)=
x^2 could be
Transformed to
F(x) =-2x^2.
Reflection across
The x axis with
A vertical
Stretch of 2
Graph
X^2-4x-5
Describe the
Domain,range,
Zeros, y-int.
End Behavior.
Domain: all real’s
Range: y or = -9
Zero’s: -1 and 5
Y-int : (0,-5)
E.B. As x app.
Pos. inf. Y app
Pos. inf. As x app
Neg. if. Y app
Pos. inf.
The vertex
Represents what
Two letters?
(h,k)
If f(x)=3^x-3.
Determine the
Horizontal
Asymptote,
Domain, and
Range.
H.A: y=-3
Domain: All reals
Range: y>-3
Ratio (r) =
(Term)/(previous
Term)
To find inverse
Given an
Equation:
1) Interchange
X and y
2) Solve for y
If f(x)=1/(x+2)
Describe the
Domain, Range,
& Asymptotes
Domain: All Real
Numbers except
-2; Range: All
Real Numbers
Except 0;
Asymptote:
X=-2
Y=0