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A Year In Review

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FC: A YEAR IN REVIEW | EPIC MATH! created by expert computer analysis specialist: Seabreeze

2: Chapter 1: Graphs, Functions, and Models Graphs provide a means of displaying, interpreting, and analyzing data in a visual format. -graphing an equation is making a drawing that represents the solutions of the given equation Intercepts -the x-intercept of a graph is a point where the graph of a given function touches the x-axis or a point where y=0 -the y intercept is a point in which the line of a given graph touches the y-axis or a point where x=0

3: Chapter 2: More on Functions Increasing, Decreasing, & Constant Functions -As you read the graph from left to right the the function is: *Increasing: if as the x-coordinates increase the y-coordinates also increase *Decreasing: if as the x-coordinates increase the y-coordinates decrease *Constant:if as the x-coordinates increase the y-coordinates stay the same Relative Max/Min -the relative max is the highest point on a parabola that is open downward while the relative min is the opposite, the lowest point on a parabola open upward.

4: Chapter 3: Quadratic Functions and Equations; Inequalities The Complex Numbers -The Number i * i = the square root of -1 * i^2 = -1 -Complex Numbers *a complex number is a number in the form of a + bi where a and b are real numbers. The number a is said to be the real part and b is the imaginary part. -Conjugates *The conjugate of a + bi is a - bi. The numbers a + bi and a - bi are complex conjugates.

5: The Principle of Zero Products: -If ab = 0 is true, then a = 0 or b = 0, and if a = 0 or b = 0, then ab = 0 The Principle of Square Roots: -If x^2 = k, then x = the square root of k or x = the negative square root of k The Principle of Powers: -For any positive integer n: *If a = b is true, then a^n = b^n is true

6: Chapter 4: Polynomial and Rational Functions Leading Term Test: -if an x^n is the leading term of a polynomial function, then the behavior of the graph as x---->infinity or as x---->negative infinity can be described in one of the four following ways

7: The Intermediate Value Theorem: -For any polynomial function P(x) with real coefficients, suppose that for a not equal to b, P(a) and P(b) are of opposite signs. Then the function has a real zero between a and b. The Remainder Theorem - If a number c is substituted for x in the polynomial f(x), then the result of f(c) is the remainder that would be obtained by dividing f(x) by x - c. That is, if f(x) = (x - c) * Q(x) + R, then f(c) = R The Factor Theorem -For a polynomial f(x), if f(c) = 0, then x - c is a factor of f(x). The Fundamental Theorem of Algebra -Every polynomial function of degree n, with n > or = 1, has at least one zero in the set of complex numbers Determining Vertical Asymptotes - For a rational function f(x) = p(x)/q(x), where p(x) and q(x) are polynomials with no common factors other than constants, if a is a zero of the denominator, then the line x = a is a vertical asymptote for the graph of the function.

8: Chapter 9: Systems of Equations and Matrices Row Equivalent Operations -1. Interchange any two rows 2. Multiply Each entry in a row by the same nonzero constant. 3.Add a nonzero multiple of one row to another row. Row-Echelon Form -1. If a row does consist entirely of 0's, then the first nonzero element in the row is a 1 (called the leading 1) 2. For any two successive nonzero rows, the leading 1 in the lower row is farther to the right than the leading 1 in the higher row 3. All the rows consisting entirely of 0's are at the bottom of the matrix If a fourth property is also satisfied, a matrix is said to be in reduced-row echelon form 4. Each column that contains a leading 1 has 0's everywhere else

9: Chapter 10.7: Parametric Equations Parametric Equations - If f and g are continuous functions of t on an interval I, then the set of ordered pairs (x, y) such that x = f(t) and y = g(t) is a plane curve. The equations x = f(t) and y = g(t) are parametric equations for the curve. the variable t is the parameter.

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