FINAL EXAM ALGEBRA 2014 DETROIT PUBLIC SAFETY ACADEMY MS. DEGAIN REVIEW MATERIALS

3 RD CARD MARKING Slope Rate of Change Functions

WHAT IS SLOPE?

REMEMBER SLOPE-INTERCEPT

WHAT IS RATE OF CHANGE? The SAME EXACT THING AS SLOPE!!!!!!

WHAT IS A FUNCTION? A relationship that will take an input and produce a given output. Domain is the x values Range is the y values The Domain cannot be repeated but the Range can. A functions will pass the vertical line test. NOT A FUNCTION BECAUSE THE X REPEATED (#5) This is a function because if you draw vertical lines through the curvy red graph it would only intersect it once.

FUNCTIONS CONTINUED There are many different types of functions Linear Quadratic Polynomial Exponential Linear functions are in Slope-Intercept form usually. Graph a line (non vertical) Quadratic functions have a power of 2. Graph a “U” Shape called a Parabola Polynomial functions have multiple terms with powers. Graph a “W” shape or wavy shape Exponential functions have a power that is a variable. Graphs look like half of a “U” shape and sharply increase or decrease.

f(x) is just like the letter y. It represents the output and range. It is NO DIFFERENT THEN THE LETTER Y WHEN GRAPHING!! If an equation has find f(2), or f(x-2) all you have to do is substitute in said values into the equation. These are the INPUTS, and inputs are the x values. Just plug them in.

4 TH CARD MARKING Systems of Equations Graphing Substitution Elimination Polynomials Adding Subtracting Multiplying Factoring Radicals Simplifying

SYSTEMS OF EQUATIONS: GRAPHING The Variable Y, must be isolated. Use slope-intercept form to graph Calculators can easily find intersection points if in slope-intercept, or you can graph by hand. What does infinite solutions graph look like? What does no solution graph look like? How do you know if the graph has one solution, no solution, or infinitely many solutions?

SUBSTITUTION METHOD When one of the equations has a variable isolated and the other one doesn’t, this is the best method to use. Take the value of one equation and plug it into the other Remember “Help the Helper” and “Help me, help you”? Simplifying is key here (take your time on correctly calculating). Don’t forget to solve for both variables, not just one.

ELIMINATION Best used when there are no variables isolated. Goal is to get opposite coefficients of one of the variables. If they are not already opposite, then use the LCM to create them. Remember to calculate and actually do the operations that you have written down.

WHAT IS A POLYNOMIAL? Many termed expression. No radicals All real numbers Cannot equal zero Monomial One Term Binomial Two Terms Trinomial Three Terms

BE CAREFUL WITH EXPONENTS Adding/Subtracting Only add/subtract like terms Remember to look at the sign in front of each term (determines whether it is positive or negative Do NOT add/subtract the exponents. Multiplying Distributive/Double Distributive Property When the variables are alike, you add the exponents. Remember to simplify by combining like terms. (combining means to add/subtract so be careful in this step.)

EXAMPLES Add/SubtractMultiplying

SIMPLIFYING RADICALS GREATEST PERFECT SQUARE FACTOR!!! Pull the square roots of numbers out in front of radical. Find square roots of variables (trick: divide exponent by 2, that will be the power of the variable on the outside of the radical). If a variable has an odd numbered exponent, there should be one variable left inside radical. If even, there shouldn’t be any left inside. Common Perfect Squares: 4, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256…