Functions, Equations, and Graphs Chapter 2

2.3 Linear Functions and Slope-Intercept Form Pg. 74 – 80 Obj: Learn how to graph linear equations and write equations of lines. A.CED.2, F.IF.4

2.3 Linear Functions and Slope-Intercept Form Slope – the ratio of the vertical change to the horizontal change Linear Function – a function whose graph is a line Linear Equation – a solution of a linear equation is any ordered pair that makes the equation true

2.3 Linear Functions and Slope-Intercept Form y-intercept – the point at which the line crosses the y-axis x-intercept – the point at which the line crosses the x-axis Slope-intercept form – y=mx + b m = slope b = y-intercept Horizontal Line – y=# Vertical Line – x=#

2.4 More About Linear Equations Pg. 81-88 Obj: Learn how to write an equation of a line given its slope and a point on the line. F.IF.8, F.IF.9, F.IF.2, A.CED.2

2.4 More About Linear Equations Point-Slope Form y – y1 = m(x – x1) Standard form of a Linear Equation Ax + By = C Parallel Lines – have the same slope Perpendicular Lines – have opposite reciprocal slopes

2.6 Families of Functions Pg. 99 – 106 Obj: Learn how to analyze transformations of functions. F.BF.3

2.6 Families of Functions Parent Function – the simplest form in a set of functions that form a family Transformation – a change made to at least one value of the parent function Translation – shifts the graph of the parent function horizontally, vertically, or both without changing shape or orientation Reflection – flips the graph of a function across a line

2.6 Families of Functions Vertical Stretch – multiplies all y-values of a function by the same factor greater than 1 Vertical Compression – reduces all y-values of a function by the same factor between 0 and 1

Transformations of f(x) 2.6 Families of Functions Transformations of f(x) Vertical Translations y=f(x) + k Shifted up k units y=f(x) – k Shifted down k units Horizontal Translations y=f(x-h) Shifted right h units y=f(x+h) Shifted left h units Vertical Stretches and Compressions y=af(x) a>1 Vertical Stretch y=af(x) 0<a<1 Vertical Compression Reflections y=-f(x) Reflected across the x-axis y=f(-x) Reflected across the y-axis

2.7 Absolute Value Functions and Graphs Pg. 107 – 113 Obj: Learn how to graph absolute value functions. F.BF.3, A.IF.7.b

2.7 Absolute Value Functions and Graphs Absolute Value Function – f(x) = |x| - the graph of the absolute value of a linear function in two variables is V-shaped and symmetric about a vertical line Axis of Symmetry – the vertical line that the absolute value function is symmetric about Vertex – either the maximum or minimum point of the absolute value function

2.7 Absolute Value Functions and Graphs The Family of Absolute Value Functions Vertical Translation y=|x| + k – Shifted up k units y=|x| - k – Shifted down k units Horizontal Translation y=|x – h| - Shifted right h units y=|x + h| - Shifted left h units Vertical Stretch and Compression y=a|x| - Vertical stretch – a>1 y=a|x| - Vertical compression – 0<a<1 Reflection y=-|x| - Across the x-axis y=|-x| - Across the y-axis

2.7 Absolute Value Functions and Graphs General Form of the Absolute Value Function y=a|x-h|+k Stretch or compression factor is |a| Vertex is (h,k) Axis of Symmetry is x=h

2.8 Two-Variable Inequalities Pg. 114 – 120 Obj: Learn how to graph two-variable inequalities. A.CED.2, F.IF.7.b

2.8 Two-Variable Inequalities Linear Inequality – an inequality in two variables whose graph is a region of the coordinate plane bounded by a line Boundary – the line in the graph of a linear inequality Half-planes – the boundary separates the coordinate plane in to these – one of the half- planes is the solution Test point – a point that is not on the boundary line

2.8 Two-Variable Inequalities Method for graphing Inequalities Graph the line <, > - dashed line <, > - solid line Choose a test point (0,0) if possible If test point is true, shade on the side with the point. If test point is false, shade on the opposite side.