S: Math 171
BC: MATH 171
FC: CREATED BY: KETURAH WILLIAMS | MY YEAR IN REVIEW
1: Linear Functions | -A linear function can be written as f(x)=mx+b , where m & b are constants. -The slope "m" of a line contains points (x,y) and (x2,y2) - M = rise over run. ( I remember that as you have to RISE first before you RUN) -Slope intercept form is y=mx+b | SLOPE
2: MATH IN THE MAKING | -The point slope equation of the line with slope "m" passing through (x,y) is : - Point slope equation: y-y1 = m(x-x1) - Parallel Lines are vertical lines that are parallel.Nonvertical lines are parallel ONLY IF they have the same SLOPE and different y-intercepts. - Perpendicular lines are two lines with slopes "m" and m2. Two lines are perpendicular ONLY IF the product of the slope is -1. | Point Slope Equation
3: Linear Equations | -An equation is a statement that two expressions are equal. To solve an equation in one variable is to find ALL the values that make the equation true. -Equations that have the same solution set are equivalent equations. Equation Solving Principles: -Addition Principle: a=b is true, then a+c=b+c is true. -Multiplication Principle: a=b is true, then ac+bc is true.
4: Symmetry & Transformations | -A knowledge of symmetry in mathematics helps us graph and analyze equations and functions. -The point (x, -y) is said to be symmetric with respect to the x-axis. -The point (-x, y) is said to be symmetric with respect to the y-axis. -The point (-x, -y) is said to be symmetric with respect to the origin.
5: Even and Odd Functions | -If the graph of a function is symmetric with respect to the y-axis, we say that it is an EVEN FUNCTION : f(x) = f(-x) -If the graph of a function is symmetric with respect to the origin, we say that it is an ODD FUNCTION : f(-x) = -f(x)
6: Quadratic Equation, Functions | - Quadratic Equations : equation that can be written in the form : ax2 +bx + c =0 , a cannot equal 0 -Equation Solving Principles is the principals of zero products: ab=0 is true, then a=0 or b=0 and if a=0 or b=0 then ab=0.
7: COMPLETING SQUARES | - | 1. Check for descending order. 2. "a" must be one. 3. Move "c" to the right 4. B * 1/2, square it, add to both sides. 5. Factor left side, combine like terms on right 6. take square root of both sides 7. Solve for x, find two answers
8: Rational Inequalities | 1. Break denominator 2. Find vertical asymptote which is the same thing as the domain. 3. Find horizontal asymptote. 4. Everywhere "x" put zero in denominator for y-intercept. 5. Graph. Find VA by dotted line by going down. Identify HA by dotted line going sideways.
9: MATH IS A BEAUTIFUL WORLD WORLD IN WHICH WE LIVE | -