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Algebra Crunchers
Coolmath's Algebra Practice Problems-
Lines, Radicals, Algebraic Fractions, Functions:

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Lines:
Finding the slope of a line given two points
Example:  Find the slope given ( -2, 5 ) and ( 7, -3 )
Finding the slope from the equation of a line
Example:  Find the slope given 2x+3y=6
Finding the equation of a line given a point and a slope
Example:  Find the equation given m = -5 and ( -6, 2 )
Finding the equation of a line given two points
Example:  Find the equation given ( -1, 3 ) and ( 8, -5 )
Finding the equation of the line that is parallel to a given line and passing through a given point
Example:  Find the equation that is parallel to 3x-5y=8 and passes through ( -2, 4 )
Finding the equation of the line that is perpendicular to a given line and passing through a given point
Example:  Find the equation that is perpendicular to 7x+6y=-3 and passes through ( 5, -2 )
Radicals:
Simplifying (reducing) radicals
Example: sqrt(75) = 5 sqrt(3)
Multiplying Radicals
Example: sqrt(8)sqrt(2)
Adding & Subtracting Radicals
Example: sqrt(12) + sqrt(3) - sqrt(27)
Rationalizing Denominators
Example: 3 / sqrt(5)
Algebraic Fractions:
Adding & subtracting algebraic fractions
Example: ( 6 / ( x^2-4 ) ) - ( 1 / ( x-2 ) )
Multiplying algebraic fractions
Example:  ( ( x^2-9 ) / ( x^2-4x+3 ) ) * ( ( x-1 ) / ( x^2+8x+15 ) )
Dividing algebraic fractions
Example:  ( ( x^2-9 ) / ( x^2-4x+3 ) ) / ( ( x^2+8x+15 ) / ( x-1 ) )
 
Function Notation:
Substituting numbers into functions
Example:  Given f(x) = 3x^2-7x+5  find f(-4)
Finding f(x+h)
Example:  Given f(x) = 3x^2-7x+5  find f(x+h)
Finding the difference quotient
Example:  Given f(x) = 3x^2-7x+5  find ( f(x+h)-f(x) ) / h
 

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