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A Year In Review

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BC: I have really enjoyed this year with you. Thank you for always being you! | Hilary Wilson

FC: A YEAR IN REVIEW | Hilary Wilson | Precalculus Algebra

1: Chapter 1.4 | slope intercept form: | y=mx+b | *parallel lines have equal slopes | y= 3/2x-8 y= 8+1.5x | *perpendicular lines have negative reciprocal slopes | y= 4x-5 y= -1/4x+2 | Equations of lines and modeling

2: "Families are like fudge ... mostly sweet with a few nuts." | Chapter 2.1 | Relative Maximum: | f(c)>f(x) ; x cannot = c | Relative Minimum: | f(c)

3: Chapter 2.4 | Symmetric with respect to the x axis: | (x,y) and (x,-y) | Symmetric with respect to the y axis: | (x,y) and (-x,y) | Symmetric with respect to the origin: | (x,y) and (-x,-y) | Symmetry and transformations

4: Chapter 10.7 | 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 | x= 1/2 t | By writing a corresponding rectangular equation, you eliminate the parameter | Parametric equations

5: Chapter 3.5 | Absolute value: write 2 math problems and remember to change the signs on the right side of the second problem | *if OR equation should overlap, then the final answer is ALL REAL NUMBERS | *if AND equation should not overlap, the final answer is NO SOLUTION | Solving equations and inequalities with absolute value

6: Chapter 4.4 | *the degree of 1 or more tells you the you have at least 1 zero in the set of complex numbers | *if a+bi is a zero of a function, the a-bi is also a zero | *for negative zeros, substitute -x for new problem | Theorems about zeros of polynomial functions

7: "The friends we meet on the path of life make the trip worth while." | Chapter 9.4 | when adding or subtracting matrices, the dimensions must be the same (rows and columns) | when multiplying matrices, the columns in the first matrix must equal the rows in the second matrix | 2x3=3x3 | answer matrix will be a 2x3 | Matrix operations

8: Chapter 9.1 | Case 1: when lines cross there is exactly 1 common point; 1 solution, consistent and independent | Case 2: when lines are parallel there is no common point; no solution, inconsistent and independent | Case 3: when lines are identical, there is infinitely many common points; infinitely many solutions, consistent and dependent

9: Chapter 4.5 | Rational Functions | Vertical Asymptote: occurs 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

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  • By: Hilary W.
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