Absolute Value 4 4 6 Make it positive 4 4 4 6 4 6 2 Properties: Commutative Associative Identity Properties • Commutative – change order x 3 3 x • Associative – change parentheses x 3 2 x (3 2) • Identity – stays the same 3(1) 3 or x0 x Combine Like Terms 3x 7 y x 2 y 2 2 Add (or subtract) the coefficients of like terms 3x 7 y x 2 y 2 x 9 y 2 2 2 Distribution 3 x 7 x 3 Multiply by every term in the parentheses 3 x 7 3x 21 x 3 1( x 3) 1x 3 Graphing Inequalities x5 x5 x5 x5 Graphing Inequalities on a number line x5 x5 x5 x5 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 Graphing Linear Inequalities • Dashed or solid line • Shade above or below Graphing Linear Inequalities Words to algebra expression • Product of 3 and a number • Quotient of 3 and a number • Sum of 3 and a number • 3 less than a number • Four times a sum of 3 and a number • Product of 3 and a number 3x • Quotient of 3 and a number 3 x • Sum of 3 and a number 3 x • 3 less than a number x 3 • Four times a sum of 3 and a number 4(3 x) Reciprocal 3 4 Reciprocal – flip top to bottom, bottom to top Reciprocal of 3 is 4 4 3 Steps to solve equations Steps to solve equations • • • • Distribute to remove parentheses Combine like terms on same side of = Move variable to left by adding opposite Move number to right by adding opposite • Divide by coefficient of variable Solving Inequalities What do I remember to do when I divide or multiply by a negative number? Example: -2x < 8 Solving Inequalities What do I remember to do when I divide or multiply by a negative number? SWITCH THE SIGN! Example: -2x < 8 2 x 8 2 2 x 4 Solving Inequalities What do I do when I solve and the variable ends up on the right? Example: 8 < x Solving Inequalities • What do I do when I solve and the variable ends up on the right? • Switch the order, switch the sign. • Example: 8 < x changes to: x>8 Solving Inequalities How do I solve a 3-part inequality? Example: 4< 2x+1 < 8 Solving Inequalities How do I solve a 3-part inequality? Get x alone in the middle, between 2 numbers. Do the same operation left, center, and right. Example: 4< 2x+1 < 8 -1 -1 -1 3 < 2x < 7 3/2 < x < 7/2 Notes about Functions • Domain is… • Range is… • f(x) means… • It’s a function if… Notes about Functions • Domain is… all the x values • Range is… all the y values • f(x) means… plug in x to get y • It’s a function if… no x’s are repeated or no points are in a vertical line. Correlation on Scatter Plots • How do I draw the trend line? • Direction of negative correlation • Direction of positive correlation y 6 5 4 3 2 1 1 2 3 4 5 6 x y 6 5 4 3 2 1 1 2 3 4 5 6 x Correlation on Scatter Plots • How do I draw the trend line? Straight through the middle • Direction of negative correlation: down to the right • Direction of positive correlation: up to the right y 6 5 4 pos 3 2 1 1 2 3 4 5 6 x y 6 5 neg 4 3 2 1 1 2 3 4 5 6 x