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FC: A YEAR IN REVIEW | Revelation in Math! | Adam Bunn
1: This Book is Dedicated to the lovely Mrs. Pitt
2: Graphing | - To graph an equation is to make a drawing that represents the solutions of an equation. - An x-intercept is a point (a,0). To find a, let y=0 and solve for x - An y-intercept is a point (0,b). To find b, let x=0 and solve for y
3: Symmetry | - Algebraic Tests of Symmetry: -x-axis: if replacing y with -y produces an equivalent equation, then the graph is symmetric with respect to the x-axis -y-axis: if replacing x with -x produces an equivalent equation, then the graph is symmetric with respect to the y-axis. -origin: if replacing x with -x and y with -y produces an equivalent equation, then the graph is symmetric with respect to the origin.
4: Variations | - Direct Variation: y=kx - Inverse Variation: y=k/x - Joint Variation: y=k(x)(z) - mostly in word problems
5: Complex Numbers | - the number i is defined such that i=square root of -1 i^2=-1 - A complex number is a number is a number of the form a+bi, where a and b are real numbers. The number a is said to be the real part of a+bi and the number b is said to be the imaginary part of a+bi
6: Quadratic Equations | - A quadratic equation is an equation that can be written in the form ax^2+bx+c=0 where a, b, and c are real numbers
7: The Remainder Theorem | - If a number c is substituted for x in the polynomial f(x), then the result 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
8: Asymptotes | -Vertical: occur at any x-values that make the denominator 0 -The x-axis is the horizontal asymptote: when the degree of the numerator is less than the degree of the denominator - A horizontal asymptote other than the x-axis: occurs when the numerator and the denominator have the same degree - An oblique asymptote: occurs when the degree of the numerator is 1 greater than the degree of the denominator
9: Parametric Equation | - 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