Algebra II Regents Review All

(Unit 2: Functions) 4 names for values when a function crosses the x-axis

X-intercepts, zeros, roots, solutions

(Unit 2: Functions) Input of a function (independent variable)

x

(Unit 2: Functions) Equation of y-axis

x = 0

(Unit 3: Linear Functions) Point-Slope form of a line

y - y1 = m(x - x1)

(Unit 2: Functions) Equation of x-axis

y = 0

(Unit 4: Exponents and Logarithms) Form of exponential functions

y = a(b)^x

(Unit 2: Functions) Function Notation

y = f(x)

(Unit 3: Linear Functions) Direct Variation

y = kx (y and x are replaced with the variables in the context of the problem)

(Unit 3: Linear Functions) Slope-Intercept form of a line

y = mx + b

(Unit 3: Linear Functions) Inverses of lines are reflected over what line?

y = x

(Unit 2: Functions) Output of a function (dependent variable)

y or f(x)

(Unit 3: Linear Functions) What is the y-intercept of a line in y = mx + b form? (Careful it's not just b!!!)

(0, b)

(Unit 1: Algebraic Essentials) Associative Property of Addition

(a + b) + c = a + (b + c)

(Unit 1: Algebraic Essentials) Distributive Property of Division

(a ± b)/c = a/c ± b/c

(Unit 1: Algebraic Essentials) Associative Property of Multiplication

(ab)c = a(bc)

(Unit 3: Linear Functions) Average rate of change formula

(f(b) - f(a))/(b - a)

(Unit 2: Functions) The slope of a horizontal line is...

0

(Unit 4: Exponents and Logarithms) Anything to the 0 power is...

1

(Unit 1: Algebraic Essentials) Term

A single number or combination of numbers and variables using exclusively multiplication or division. (Ex: x^2, x/2, 3x, 7)

(Unit 2: Functions) Vertical Line Test

A test used to determine whether a relation is a function by checking if a vertical line touches 2 or more points on the graph of a relation

(Unit 1: Algebraic Essentials) Multiplying Terms

Multiply coefficients and add powers (Ex: (4x^3y^2)(5xy^5) = 20x^4y^7)

(Unit 1: Algebraic Essentials) Inconsistent (null set, expressed with {} or Ø)

No solutions (Ex: 2x + 5 = 2x - 1)

(Unit 4: Exponents and Logarithms) Method of common bases

One way to solve for a variable as an exponent. Change terms to the same base. You can eliminate same bases.

(Unit 2: Functions) On a number line an __________ circle represents exclusivity

Open

(Unit 2: Functions) Use these for exclusivity

Parentheses ( )

(Unit 3: Linear Functions) Answers to a 3x3 system of equations should be written in...

Parentheses (x, y, z)

(Unit 2: Functions) Maximum Value

The highest y-value

(Unit 2: Functions) Minimum Value

The lowest y-value

(Unit 2: Functions) Inverses of functions

The x and y coordinates are switched (x,y) -> (y,x). The input of a function is the output of its inverse.

(Unit 3: Linear Functions) y-intercept

Where the function crosses the y-axis (x = 0)

(Unit 3: Linear Functions) Steps to solve 3x3 systems of equations

1- Start with any two equations to eliminate a variable. Choose the easiest variable to eliminate. Then choose a different pair of equations and eliminate the same variable. You will be left with a 2x2 system. 2- Now, solve the new 2x2 system by elimination. 3- Substitute your known value into one of your 2x2 system equations to solve for the other variable. 4- Substitute your two known variables into any equation with all 3 variables. Solve for the final variable. 5- Check your work with your calculator and/or substituting these values into several of the equations. 6- Write the values in parentheses (x, y, z). *Note- you may need to multiply both sides of an equation by a number to help eliminate variables.

(Unit 4: Exponents and Logarithms) Taking the nth root of a number is the same as raising that number to the _________ power.

1/n

(Unit 1: Algebraic Essentials) Equations have THIS that makes them different from expressions

=

(Unit 2: Functions) Function

A "rule" that assigns exactly one output (y-value) for each input (x-value).

(Unit 1: Algebraic Essentials) Expression

A combination of terms using addition and subtraction. (Ex: 2x^2 + 3x - 7)

(Unit 2: Functions) One-to-one function

A function where each input has one unique output

(Unit 3: Linear Functions) What is (x1, y1) for point-slope form?

A given point

(Unit 1: Algebraic Essentials) Variable

A quantity that is unknown, unspecified, or can change within the context of the problem. Most often presented by a letter or symbol (such as x).

(Unit 2: Functions) Relative maximum/minimum

Any high/low value on the graph.

(Unit 2: Functions) Use these for inclusivity

Brackets [ ]

(Unit 2: Functions) On a number line a __________ circle represents inclusivity.

Closed

(Unit 1: Algebraic Essentials) Multiplying Polynomials

Distribute to multiply each term (Ex: (2x + 1)^2 = (2x + 1)(2x + 1) = 4x^2 + 4x + 1

(Unit 3: Linear Functions) Solving systems by elimination

Eliminate one variable by adding/subtracting lines of a system of equations

(Unit 2: Functions) When asked for an interval of values where y > 0, are the x-intercepts included or excluded?

Excluded

(Unit 2: Functions) When infinity and negative infinity are included in a domain or range, they are ALWAYS marked with __________.

Exclusivity ( )

(Unit 1: Algebraic Essentials) Monomial

Expression with 1 term

(Unit 1: Algebraic Essentials) Binomial

Expression with 2 terms

(Unit 1: Algebraic Essentials) Trinomial

Expression with 3 terms

(Unit 1: Algebraic Essentials) Polynomial

Expression with more than 3 terms

(Unit 1: Algebraic Essentials) Multiplying Two Binomials

FOIL (First, Outer, Inner, Last)

(Unit 1: Algebraic Essentials) Simplest form is _________ ______ (leave final answers in this form!)

Factored form

(Unit 2: Functions) How to you read the following: (a, b]

From a exclusive to b inclusive

(Unit 3: Linear Functions) Piecewise Functions

Functions that involve different equations for different portions of their domains

(Unit 2: Functions) Horizontal line test

If any given horizontal line passes through the graph of a function at most one time, then that function is one-to-one

(Unit 3: Linear Functions) Solving systems by substitution

If you know the value of one of variables in terms of the others, you can substitute this value for that variable into the system

(Unit 2: Functions) When asked for a domain for increasing/decreasing the relative min/max are marked with __________.

Inclusivity [ ]

(Unit 1: Algebraic Essentials) Identity (Expressed with ∞)

Infinitely many solutions (Ex: 2x + 9 = 2x + 9)

(Unit 4: Exponents and Logarithms) b^n means...

Multiply b by itself n times

(Unit 4: Exponents and Logarithms) PPP (Ex: 2^5^2 = 2^10)

Power to a power is a product (multiply the exponents)

(Unit 4: Exponents and Logarithms) Rational Exponents

Power/Root

(Unit 3: Linear Functions) How to write equation of a line given the slope and a point

Substitute x, y, and m into point-slope formula, then simplify to solve for y.

(Unit 1: Algebraic Essentials) Exponents mean...

Repeated multiplication

(Unit 4: Exponents and Logarithms) When simplifying rational exponents (power/root), does power or root come first?

Root

(Unit 2: Functions) What does the f mean in f(x)?

Rule/Function

(Unit 4: Exponents and Logarithms) The a in y = a(b)^x is the...

Scalar multiple

(Unit 2: Functions) Domain

Set of all x-values

(Unit 2: Functions) Range

Set of all y-values

(Unit 3: Linear Functions) How to find the solutions to two functions

Set them equal to each other

(Unit 2: Functions) When you plug in a number into a function it is called __________.

Substitution

(Unit 3: Linear Functions) How to convert point-slope form to slope-intercept form

Simplify and solve for y

(Unit 2: Functions) How to solve for the inverse of a function

Switch x and y, then solve for y

(Unit 1: Algebraic Essentials) Tabular Method

Table used for multiplying two polynomials. Loop all like terms.

(Unit 4: Exponents and Logarithms) b^-n means...

The reciprocal of b^n (b^-n = 1/b^n)

(Unit 1: Algebraic Essentials) Solution Set (Expressed with solutions in braces {})

The set of all values of the variable that make the equation true

(Unit 1: Algebraic Essentials) Like Terms

Two or more terms that have the same variables raised to the same powers. Only the coefficients can differ. (Ex: 4x^2y and 6x^2y)

(Unit 3: Linear Functions) Union in interval notation

U

(Unit 2: Functions) The slope of a vertical line is...

Undefined

(Unit 3: Linear Functions) How to write equation of a line given two points

Use average rate of change formula to find m, then substitute that value, and x and y from one of the points into point slope formula, then simplify to solve for y.

(Unit 2: Functions) Interval notation

Used to express domain and range of functions

(Unit 2: Functions) Function Composition

Using the output of one function as the input of another function

(Unit 2: Functions) If a function passes the horizontal line test, its inverse passes the...

Vertical Line Test

(Unit 2: Functions) Undefined

When the denominator = 0

(Unit 2: Functions) Decreasing

Y decreases as x increases

(Unit 2: Functions) Increasing

Y increases as x increases

(Unit 3: Linear Functions) How to find the y-intercept

Zero the x

(Unit 3: Linear Functions) How to find x-intercepts/zeros/roots/solutions

Zero the y

(Unit 1: Algebraic Essentials) Commutative Property of Addition

a + b = b + a

(Unit 1: Algebraic Essentials) Distributive Property of Multiplication

a(b ± c) = ab ± ac

(Unit 1: Algebraic Essentials) Commutative Property of Multiplication

ab = ba

(Unit 4: Exponents and Logarithms) When you multiply two terms with the same base you __________ the exponents. (Ex: 2^4 + 2^2 = 2^6)

add

(Unit 3: Linear Functions) What letter from y = mx + b represents the y-coordinate of the y-intercept?

b

(Unit 4: Exponents and Logarithms) Anything to the 1st power is...

itself

(Unit 3: Linear Functions) Constant of variation

k

(Unit 2: Functions) f(g(x)) or f o g(x)

f follows g(x)

(Unit 2: Functions) Inverse Function Notation

f^-1(x)

(Unit 2: Functions) g(f(x)) or g o f(x)

g follows f(x)

(Unit 3: Linear Functions) What letter from y = mx + b represents the slope?

m

(Unit 3: Linear Functions) What values does m have to be if the linear function is decreasing?

m < 0

(Unit 3: Linear Functions) What values does m have to be if the linear function is increasing?

m > 0

(Unit 4: Exponents and Logarithms) When you divide two terms with the same base you __________ the exponents. (Ex: 2^4/2^2 = 2^2)

subtract