Section 1
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Dividing rational expressions
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Last updated
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Date created
Mar 1, 2020
Cards (54)
Section 1
(50 cards)
Dividing rational expressions
1)Keep the first term 2)Change division to multiplication 3)Flip second term (to get reciprocal)
Function notation
y=f(x) y=output f=Name of function x=input
Domain
All possible values of the independent variable(input)
Rational numbers
Can be written as a fraction or a decimal which is repeating
Special line: Vertical
If a line crosses X-AXIS we write x=?
Range
All possible values of the dependent variable(output)
Number sentence
A specific type of algebraic equation. It is an algebraic expression that only has numbers (NO VARIABLES)
When a<o
Opens downwards :(
Multiplying rational expressions
1)Factor 2)Cancel all common factors in the numerator and denominator 3)Multiply straight across
Parallel line
Do NOT intersect; they have the same slope but DIFFERENT Y-INTERCEPTS.
Lines are parallel
No solution, same slopes, different y-intercepts
Special line: Horizontal
If a line crosses Y_AXIS, we write y=?
Integers
Positive and negative whole numbers
Steps to simplify rational expressions
1)Factor what is possible in numerator & denominator 2)Reduce!
To solve quadratic equation
•Rewrite equation in standard form •Factor •Set each factor equal to 0 •Check each solution with equation
Perimeter
2L+2W
When a>0
Opens upward :)
Algebraic expression
A mathematical phrase that can include numbers, variables, and operation symbols
Finding terms in arithmetic sequence
an = a1 + (n - 1)d
To factor COMPLETELY
•Check for a GCF and factor it out if possible •Factor further if possible (different of perfect squares or a quadratic trinomial) •Check by multiplying using the distribution property
Function
A relation in which each element of the domain is paired with exactly one element of range. (If DOMAIN is chosen more than once, it is NOT A FUNCTION) •In a function, a vertical line intersects the graph only ONCE(The vertical line test)
To simplify radicals
•Find the largest perfect square which is a factor of the radicand •Rewrite the square root as a product of a perfect square and another factor •Evaluate the square root of the perfect square and write as a coefficient •Keep the other factor as a radicand. Ex: √50= √25 √2 => 5√2
Inequality
A mathematical statement that contains an inequality symbol (!!! Whenever you MULTIPLY or DIVIDE an inequality by a NEGATIVE NUMBER, you MUST FLIP the inequality sign!!!)
!Checklist for graphing a line from an equation!
•Label x and y axis •Connect at least 2 points with a STRAIGHT EDGE •Draw arrows at both ends of the line •Label the line with the equation
Polynomial
•An algebraic expression with one or more terms •The prefix POLY means MANY
To factor difference of perfect squares, REMEMBER:!
•The numerical coefficient has to be a perfect square •And the exponent of each variable has to be an EVEN NUMBER.
Algebraic equation
Any sentence with an equal sign
Dashed line
< and >
Standard form of quadratic function
y=ax^2+bx+c
Elimination Method
1)Line up the variables 2)Find the variable with opposite coefficient 3)Add the equations to ELIMINATE the variable 4)Solve the new equation 5)Find the other variable by substitution 6)Check!
Variable
A symbol (usually a letter) representing one or more unknown numbers
Factoring y=ax^2+bx+c the x-box way
1)Find a*c (product of first and last term) 2)Find 2 new factors 3)Fill in the box
The ___________________ depends on the ______________________
Dependent variable(output), independent variable(input)
Whole numbers
Natural numbers including 0
Solid line
<= and >=
To complete the square
1)Find one half of b-> b/2 2)Square what you got from step 1 3)Add the result to the original expression
Irrational numbers
Cannot be expressed as a fraction, they are non-repeating or non-terminating decimals.
Quadratic
Linear system is made up of a quadratic equation (palabra) and a linear equation
Quadratic formula
x=-b+-√b^2-4ac/2a
The axis of symmetry
The vertical line that cuts a function down the middle.
Quadratic equation
•ax^2+bx+c=0 •The solution(s) to this are called ROOTS or ZEROS of the function (solution are x-intercept)
Natural numbers
Counting numbers greater than 0
Finding the axis of symmetry & vertex
x=-b/2x
Dependent variable
Y
Independent variable
X
Cubic Functions
•Are functions with a degree of 3 •Standard form= ax^3+bx^2+cx+d (a CANNOT equal 0)
Lines intersected
One solution, different slopes, different y-intercepts
Dinding the _______ is the same as finding the ______________________
Slope, average rate of change
Step function
A piece-wise function defined by CONSTANT values over its domain. The graph of a step function consists of a series of line segments.
Linear equation
An equation whose graph in a line. The points on the line are SOLUTIONS of the equation.
Section 2
(4 cards)