# Exam 3 Study Guide
Glossary of Key Terms

Simplify: To rewrite an expression in a less complex form, typically by combining like terms, canceling common factors, or performing operations.
Common Denominator: A denominator that is the same for two or more fractions, allowing them to be added or subtracted. The least common denominator (LCD) is the smallest such denominator.
Distribute: To multiply a factor across all terms within a set of parentheses, e.g., $a(b + c) = ab + ac$.
Combine Like Terms: To add or subtract terms that have the same variable raised to the same power.
Isolate the Variable: To manipulate an equation using algebraic operations so that the variable you are solving for is alone on one side of the equation.
Function Division ($(g/f)(x)$): An operation on two functions where the result is a new function whose value at any point $x$ is the quotient of the values of the two original functions at that point: $\frac{g(x)}{f(x)}$.
Function Composition ($(f \circ g)(x)$): An operation where one function is applied to the result of another function. $(f \circ g)(x) = f(g(x))$.
Outside Function: In a composite function $f(g(x))$, the function $f$ that is applied to the result of the inside function.
Inside Function: In a composite function $f(g(x))$, the function $g$ whose output is the input for the outside function.
Zero Product Property: A property stating that if the product of two or more factors is equal to zero, then at least one of the factors must be equal to zero.
Factor (Factoring): To express a number or polynomial as a product of its factors. Factoring a polynomial involves finding simpler polynomials whose product is the original polynomial.
Quadratic Formula: A formula used to find the solutions (roots) of a quadratic equation in the form $ax^2 + bx + c = 0$: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$.
Leading Term (of a polynomial): The term in a polynomial that has the highest degree (the highest power of the variable).
Leading Coefficient (of a polynomial): The coefficient (the numerical part) of the leading term.
Degree (of a polynomial): The highest power of the variable in the polynomial.
Zero (Root) of a Polynomial: A value of the variable that makes the polynomial equal to zero. These are the x-intercepts of the graph of the polynomial function.
Multiplicity (of a zero): The number of times a particular factor $(x - c)$ appears in the factored form of a polynomial, where $c$ is a zero of the polynomial. It affects the behavior of the graph at the x-intercept.
End Behavior (of a graph): The trend of the graph of a function as the input values (x) approach positive or negative infinity. For polynomials, this is determined by the leading term.
Bounce (at an x-intercept): The behavior of the graph of a polynomial where it touches the x-axis at a zero but does not cross it. This occurs at zeroes with even multiplicity.
Cross (at an x-intercept): The behavior of the graph of a polynomial where it passes through the x-axis at a zero. This occurs at zeroes with odd multiplicity.