- arrow notation
- a way to symbolically represent the local and end behavior of a function by using arrows to indicate that an input or output approaches a value

- axis of symmetry
- a vertical line drawn through the vertex of a parabola around which the parabola is symmetric; it is defined by$\text{\hspace{0.17em}}x=-\frac{b}{2a}.$

- coefficient
- a nonzero real number multiplied by a variable raised to an exponent

- complex conjugate
- the complex number in which the sign of the imaginary part is changed and the real part of the number is left unchanged; when added to or multiplied by the original complex number, the result is a real number

- complex number
- the sum of a real number and an imaginary number, written in the standard form$$\text{\hspace{0.17em}}a+bi,\text{\hspace{0.17em}}$$where$\text{\hspace{0.17em}}a\text{\hspace{0.17em}}$is the real part, and$\text{\hspace{0.17em}}bi\text{\hspace{0.17em}}$is the imaginary part

- complex plane
- a coordinate system in which the horizontal axis is used to represent the real part of a complex number and the vertical axis is used to represent the imaginary part of a complex number

- constant of variation
- the non-zero value$\text{\hspace{0.17em}}k\text{\hspace{0.17em}}$ that helps define the relationship between variables in direct or inverse variation

- continuous function
- a function whose graph can be drawn without lifting the pen from the paper because there are no breaks in the graph

- degree
- the highest power of the variable that occurs in a polynomial

- Descartes’ Rule of Signs
- a rule that determines the maximum possible numbers of positive and negative real zeros based on the number of sign changes of$\text{\hspace{0.17em}}f(x)\text{\hspace{0.17em}}$and$\text{\hspace{0.17em}}f(-x)\text{\hspace{0.17em}}$

- direct variation
- the relationship between two variables that are a constant multiple of each other; as one quantity increases, so does the other

- Division Algorithm
- given a polynomial dividend$\text{\hspace{0.17em}}f(x)\text{\hspace{0.17em}}$ and a non-zero polynomial divisor$\text{\hspace{0.17em}}d(x)\text{\hspace{0.17em}}$ where the degree of$\text{\hspace{0.17em}}d(x)\text{\hspace{0.17em}}$ is less than or equal to the degree of$\text{\hspace{0.17em}}f(x),\text{\hspace{0.17em}}$ there exist unique polynomials$\text{\hspace{0.17em}}q(x)\text{\hspace{0.17em}}$ and$\text{\hspace{0.17em}}r(x)\text{\hspace{0.17em}}$ such that$\text{\hspace{0.17em}}f(x)=d(x)q(x)+r(x)\text{\hspace{0.17em}}$ where$\text{\hspace{0.17em}}q(x)\text{\hspace{0.17em}}$ is the quotient and$\text{\hspace{0.17em}}r(x)\text{\hspace{0.17em}}$ is the remainder. The remainder is either equal to zero or has degree strictly less than$\text{\hspace{0.17em}}d(x).\text{\hspace{0.17em}}$

- end behavior
- the behavior of the graph of a function as the input decreases without bound and increases without bound

- Factor Theorem
- $\text{\hspace{0.17em}}k\text{\hspace{0.17em}}$is a zero of polynomial function$\text{\hspace{0.17em}}f(x)\text{\hspace{0.17em}}$if and only if$\text{\hspace{0.17em}}(x-k)\text{\hspace{0.17em}}$ is a factor of$\text{\hspace{0.17em}}f(x)$

- Fundamental Theorem of Algebra
- a polynomial function with degree greater than 0 has at least one complex zero

- general form of a quadratic function
- the function that describes a parabola, written in the form$\text{\hspace{0.17em}}f(x)=a{x}^{2}+bx+c,\text{\hspace{0.17em}}$where$\text{\hspace{0.17em}}a,b,\text{\hspace{0.17em}}$and$\text{\hspace{0.17em}}c\text{\hspace{0.17em}}$are real numbers and$\text{\hspace{0.17em}}a\ne 0.$

- global maximum
- highest turning point on a graph;$\text{\hspace{0.17em}}f(a)\text{\hspace{0.17em}}$ where$\text{\hspace{0.17em}}f(a)\ge f(x)\text{\hspace{0.17em}}$ for all$\text{\hspace{0.17em}}x.$

- global minimum
- lowest turning point on a graph;$\text{\hspace{0.17em}}f(a)\text{\hspace{0.17em}}$ where$\text{\hspace{0.17em}}f(a)\le f(x)\text{\hspace{0.17em}}$ for all$\text{\hspace{0.17em}}x.$

- horizontal asymptote
- a horizontal line$\text{\hspace{0.17em}}y=b\text{\hspace{0.17em}}$where the graph approaches the line as the inputs increase or decrease without bound.

- imaginary number
- a number in the form$\text{\hspace{0.17em}}bi\text{\hspace{0.17em}}$where$\text{\hspace{0.17em}}i=\sqrt{-1}$

- Intermediate Value Theorem
- for two numbers$\text{\hspace{0.17em}}a\text{\hspace{0.17em}}$ and$\text{\hspace{0.17em}}b\text{\hspace{0.17em}}$ in the domain of$\text{\hspace{0.17em}}f,\text{\hspace{0.17em}}$ if$\text{\hspace{0.17em}}a<b\text{\hspace{0.17em}}$ and$\text{\hspace{0.17em}}f\left(a\right)\ne f\left(b\right),\text{\hspace{0.17em}}$ then the function$\text{\hspace{0.17em}}f\text{\hspace{0.17em}}$ takes on every value between$\text{\hspace{0.17em}}f\left(a\right)\text{\hspace{0.17em}}$ and$\text{\hspace{0.17em}}f\left(b\right);\text{\hspace{0.17em}}$ specifically, when a polynomial function changes from a negative value to a positive value, the function must cross the$\text{\hspace{0.17em}}x\text{-}$axis

- inverse variation
- the relationship between two variables in which the product of the variables is a constant

- inversely proportional
- a relationship where one quantity is a constant divided by the other quantity; as one quantity increases, the other decreases

- invertible function
- any function that has an inverse function

- joint variation
- a relationship where a variable varies directly or inversely with multiple variables

- leading coefficient
- the coefficient of the leading term

- leading term
- the term containing the highest power of the variable

- Linear Factorization Theorem
- allowing for multiplicities, a polynomial function will have the same number of factors as its degree, and each factor will be in the form $\text{\hspace{0.17em}}(x-c),\text{\hspace{0.17em}}$ where$\text{\hspace{0.17em}}c\text{\hspace{0.17em}}$is a complex number

- multiplicity
- the number of times a given factor appears in the factored form of the equation of a polynomial; if a polynomial contains a factor of the form$\text{\hspace{0.17em}}{(x-h)}^{p},$ $\text{\hspace{0.17em}}x=h\text{\hspace{0.17em}}$ is a zero of multiplicity$\text{\hspace{0.17em}}p.$

- polynomial function
- a function that consists of either zero or the sum of a finite number of non-zero terms, each of which is a product of a number, called the coefficient of the term, and a variable raised to a non-negative integer power.

- power function
- a function that can be represented in the form$\text{\hspace{0.17em}}f(x)=k{x}^{p}\text{\hspace{0.17em}}$ where$\text{\hspace{0.17em}}k\text{\hspace{0.17em}}$ is a constant, the base is a variable, and the exponent,$\text{\hspace{0.17em}}p,\text{\hspace{0.17em}}$ is a constant

- rational function
- a function that can be written as the ratio of two polynomials

- Rational Zero Theorem
- the possible rational zeros of a polynomial function have the form$\text{\hspace{0.17em}}\frac{p}{q}\text{\hspace{0.17em}}$where$\text{\hspace{0.17em}}p\text{\hspace{0.17em}}$is a factor of the constant term and$\text{\hspace{0.17em}}q\text{\hspace{0.17em}}$is a factor of the leading coefficient.

- Remainder Theorem
- if a polynomial$\text{\hspace{0.17em}}f(x)\text{\hspace{0.17em}}$is divided by$\text{\hspace{0.17em}}x-k,\text{\hspace{0.17em}}$then the remainder is equal to the value$\text{\hspace{0.17em}}f(k)\text{\hspace{0.17em}}$

- removable discontinuity
- a single point at which a function is undefined that, if filled in, would make the function continuous; it appears as a hole on the graph of a function

- smooth curve
- a graph with no sharp corners

- standard form of a quadratic function
- the function that describes a parabola, written in the form$\text{\hspace{0.17em}}f(x)=a{(x-h)}^{2}+k,\text{\hspace{0.17em}}$where$\text{\hspace{0.17em}}\left(h,\text{}k\right)\text{\hspace{0.17em}}$is the vertex.

- synthetic division
- a shortcut method that can be used to divide a polynomial by a binomial of the form$\text{\hspace{0.17em}}x-k\text{\hspace{0.17em}}$

- term of a polynomial function
- any$\text{\hspace{0.17em}}{a}_{i}{x}^{i}\text{\hspace{0.17em}}$ of a polynomial function in the form$\text{\hspace{0.17em}}f(x)={a}_{n}{x}^{n}+{a}_{n-1}{x}^{n-1}+\mathrm{...}+{a}_{2}{x}^{2}+{a}_{1}x+{a}_{1}$

- turning point
- the location at which the graph of a function changes direction

- varies directly
- a relationship where one quantity is a constant multiplied by the other quantity

- varies inversely
- a relationship where one quantity is a constant divided by the other quantity

- vertex
- the point at which a parabola changes direction, corresponding to the minimum or maximum value of the quadratic function

- vertex form of a quadratic function
- another name for the standard form of a quadratic function

- vertical asymptote
- a vertical line$\text{\hspace{0.17em}}x=a\text{\hspace{0.17em}}$where the graph tends toward positive or negative infinity as the inputs approach$\text{\hspace{0.17em}}a$

- zeros
- in a given function, the values of$\text{\hspace{0.17em}}x\text{\hspace{0.17em}}$at which$\text{\hspace{0.17em}}y=0,\text{\hspace{0.17em}}$also called roots