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Algebra 2

Semester 1 final

Natural Numbers Counting numbers(1,2,3,4)
Real Numbers Any number
Reciprocals( Multiplicative Inverse) Get 1 for an answer
Closure Property A+b is a real #, ab is a real #
Commutative Property a+b= b+a
Associative Property (a+b) + c= a + (b+c), (ab)c= a(bc)
Identity Property a+ 0 =a, a* 1= 1
Inverse Property a+(-a)=0, a*1/a= 1
Distributive Property a(b+c)= ab+ac
Relation Set of pairs of input and output values
Domain Set of all inputs(x-values)
Range Set of all outputs(y-values)
Function Relation which each input has exactly one output
Vertical Line Test If a vertical line passes through 2 or more points on a graph then the relation is not a function
Linear Equation First degree equation
Linear Function Function graph is in a line
Slope- Intercept Form y=mx+b
Point- Slope Form y-y1=m(x-x1)
Standard Form Ax+By=c
X intercept y=0
Y intercept x=0
Hoy Horizontal, 0 slope, equation is y=#
Vux Vertical, undefined slope, equation is x=#
Independent Solution Has one solution
Dependent Solution Infinite Solutions
Inconsistent Solution No solution
Same slope, same y int. Dependent
Same slopes, diff y int. Inconsistent
Different slopes, different y int. Independent
Substitution Solve 1 equation for 1 of variables. Substitute equation into other equation and solve. Substitute answer into one of the original equations.
Elimination Method Line up variables and constants. Make coefficients of 1 variables opposites by multiplying entire equation by something. Add 2 equations together. Solve for left over variable. Substitute.
Elimination with 3 Equations Use 2 equations to eliminate 1 variable. Use 2 other equations the same variable. Use 2 new equations with 2 variables to solve like before.
Sin Opposite/Hypotenuse
Csc Hypotenuse/Opposite
Zero Matrix All elements equal 0(Identity property of addition)