In this video lesson we will learn how to graph an absolute value function. We will discover that the parent function is y=|x|. We will learn that all absolute value functions have a vertex which is the point the function changes direction. We will learn about vertex form of an absolute value function and how to identify the vertex. We will discover that all absolute value functions have an line of symmetry that passes through the vertex. We will learn that the vertex is (h, k) when written in vertex form. We will learn that the value h determines if the function is horizontally translated left or right. We will learn that the value a determines if the function is a stretch, shrink and/or a reflection. We will learn that the value k determines if the function is vertically translated up or down. We will also learn how to identify the domain and range of an absolute value function.
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00:00 Introduction
00:43 Graph of an Absolute Value Function
02:12 Vertex Form of an Absolute Value Function
03:15 Transformations of Absolute Value Functions
06:01 Graphing an Absolute Value Function
08:15 Student Practice #1
10:14 Student Practice #2
12:36 Student Practice #3
15:02 Student Practice #4
16:53 Student Practice #5
Common Core Math Standards
HS.A.CED.A.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
Represent and solve equations and inequalities graphically.
HS.A.REI.D.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).
HS.F.IF.C.7.B Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
Build new functions from existing functions.
HS.F.BF.B.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.