Algebra 2 Final Review
Terms in this set (147)
system of two linear equations
two variables x and y also called a linear system consists of two equations
(x,y), a point on a graph
exactly one solution
infinitely many solution
no solution graph
system of linear inequalities
answer to a system of linear inequalities
the area shaded by both graphs
system of three linear equations
a system consisting of three linear equations in three variables
Numbers that cannot be written as fractions, go on forever
Any number that can be expressed as a fraction
Positive and negative whole numbers
Natural numbers ( counting numbers) and zero; 0, 1, 2, 3...
switching of signs
power; 3^4 it is the 4
3^4; it is the 3
the parts of an expression that are added together
A letter used to represent one or more numbers
a term with no variables
The number in front of a variable
A mathematical sentence that contains an equals sign.
an equation whose graph is a line
equations that have the same solution
is an equation that relates two or more quantities
can be formed by replacing the equal sign in a linear equation with an inequality symbol
Two or more inequalities joined together by "and" or "or"
inequalities that have the same solution
The distance a number is from zero on a number line
A function that can be written as a polynomial divided by a polynomial.
If the exponent in the denominator is larger than the exponent in the numerator; m<n, then...
the line has a horizontal asymptote at y=0.
If the exponent in the numerator is larger than the exponent in the denominator; m>n, then...
the graph has no horizontal asymptote.
If the exponents values are equal in the numerator and denominator then, m=n, then....
then the line has a horizontal asymptote at y=a/b where a and b are the leading coefficients.
the numerator and denominator have no common factors.
The multiplicative inverse of a number
to add or subtract rational exponents
the denominators need to be the same.
is a fraction that contains a fraction in its numerator or denominator
solve a rational equation when each side of the equation is a single rational expression.
rational function graph
Least common Denominator
The least common multiple of the denominators of two or more fractions.
a horizontal line that the curve approaches but never reaches
A vertical line that a graph approaches but never reaches.
a function of the form f(x) = ab^x, where a and b are real numbers with a ≠ 0, b>0, and b ≠ 1
Exponential Growth Function
A function of the form y=ab^x, where b is greater than 1 and a is greater than zero
the b value of a growth function, greater than 1
is a line a graph approaches
Exponential Decay Function
y = ab^x if a > 0 and 0 < b < 1
the b value of a decay function, between 0 and 1
logarithm of y with base b
The expression y = logb x is a logarithmic function
base 10 log
base e or ln
product property of logarithms
logb mn = logb m + logb n
Quotient Property of logarthims
logb (m/n) = logb m - logb n
Power Property of logarthims
logb m^n = nlogb m
equations in which variable expressions occur as exponents
equations that involve logarithms of variable expressions
index of a radical
the value of n in the radical ^n√a
An idea similar to that of a square root, except that the root must be cubed
A relation formed by reversing x and y in a function.
a polynomial function with the highest power being three
a function in which the greatest power of the variable is 2
composition of a function
a function that contains a radical with a variable in its radicand
radical expressions that have the same index and radicand
What is the index of 3^(5/3)
The index is 3
What are the shifts of the following y=2√(x-1)+3
up 3, right 1, and stretched by 2
What are the shifts of the following y=2√(x+3)-1
down 1, left 3, and stretched by 2
Product of Powers
a^m * a^n = a^m+n
Power of a power
(a^m)^n = a^mn
Power of a product
(ab)^m = a^m b^m
a^-n = 1/a^n
a^0 = 1
Quotient of powers
a^m/a^n = a^m-n
Power of a Quotient
is a monomial or the sum of monomials
a function that is represented by a polynomial equation
number in front of the highest degree
term without a variable
degrees decrease going left to right
polynomial witha degree of 0
polynomial with a degree of 1
polynomial with a degree of 2
polynomial with a degree of 3
polynomial with a degree of 4
the shortcut for long division of polynomials when dividing divisors of the form x - k
Long dividing equations by binomials to find the roots
The turning point
Axis of Symmetry
divides the parabola into mirror images; passes though the vertex
roots, zeros, x-intercepts
Solutions to a quadratic equation
place to graph complex numbers
absolute value of a complex number
completing the square
A relation for which each input has exactly one output
a mapping, or pairing, of input values with output values
a function in the form y=mx+b
rate of change, rise over run
two lines who don't intersect; same slope
Two lines who cross at 90 degrees, opposite reciprocal slope
where the graph crosses the y-axis; x=0
where the graph crosses the x-axis; y=0
slope is 0
Slope is undefined