1. Functions, Equations, and Graphs
Chapter 2

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

3. 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

4. 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=#

5. 2.4 More About Linear EquationsPg
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

6. 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

7. 2.6 Families of Functions Pg. 99 – 106
Obj: Learn how to analyze transformations of functions.
F.BF.3

8. 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

9. 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

10. 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) <a<1 Vertical Compression
Reflections
y=-f(x) Reflected across the x-axis
y=f(-x) Reflected across the y-axis

11. 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

12. 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

13. 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

14. 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

15. 2.8 Two-Variable Inequalities
Pg. 114 – 120
Obj: Learn how to graph two-variable inequalities.
A.CED.2, F.IF.7.b

16. 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

17. 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.