# graphing absolute value functions notes

Graph Absolute Value Equations Notes. Highlights common student mistakes and points out how to … Its slope is m = 1 on the right side of the vertex, and m = - 1 on the left side of the vertex. The solution set of the equation | x| = 3 is {3, –3}, because |3| = 3 and |–3| = 3. Determine the vertex, domain, and range. Please begin working on your practice: for each label whether it is a piecewise, absolute value, or step function. Now that the equation has been simplified to y = |1/2 (x - 6)| - 10, you can get to graphing. First, we will start discussing graphing equations by introducing the Cartesian (or Rectangular) coordinates system and illustrating use of the coordinate system to graph lines and circles. Example 2. Example 1. Pages 372 - … 1) Isolate the absolute value. The graph of the absolute value function resembles a letter V. It has a corner point at which the graph changes direction. The vertex of the graph of f ()xx= is ()0, 0 . Graphing Absolute Value Functions MCC9-12.F.IF.4For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities and sketch graphs showing key features given verbal description of the relationship. Then check your The graph of a function with a horizontal (y = 0), vertical (x = 0), and oblique asymptote (purple line, given by y = 2x). DEL VALLE: Name_ ID: 1 ©N x2H0j2F0M ^KQuytnaK CSLohfQtwwmawrRex \L^LcCe.X c … Subtract 4 from each side. Title: Piecewise, Absolute Value, and Step Functions Note: Graphing an absolute value equation can be complicated, unless you know how to dissect the equation to find and use the slope and translations. Graph using a table. 1) Isolate the absolute value: ** The steps are the same as if you were getting the x by itself. In class, we use Method #2 particularly when f(x) is a quadratic function. A curve intersecting an asymptote infinitely many times. Class Notes. In this chapter we’ll look at two very important topics in an Algebra class. 2014 A Review Solutions . The range is y ≥ 0. 1) 12y=3x 2) −10y=5x 3) 3 4 y=15x y= 1 4 x y=− 1 2 x y=20x KEY CONCEPTS AND VOCABULARY Direct Variation- a linear function defined by an equation of the form y=kx, where k ≠ 0. Notes: Vertex Form of an Absolute Value Function An absolute value function written in the form g()xaxhk=−+, where a ≠ 0, is in vertex form. Graph Piecewise Functions (4.4 YL) Worksheet Key. Graph Absolute Value Equations Worksheet Key. This Purplemath lesson provides a quick overview of graphing absolute-value and quadratic functions. Constant of Variation - k, where k = y/x GRAPHS OF DIRECT VARIATIONS NOTES and EXAMPLES We’ve focused our attention this year on working with linear equations. 2014 Absolute Value Test Review. Your Algebra 2 Honors students will have foldables, guided notes, homework, and a content quiz in the Absolute Value Functions & Graphs lesson of a nine lesson unit on Functions, Equations & Graphs that cover the concepts in depth.Students will be able to:★ Graph absolute value functions★ Wr Graph the absolute value function given below. How to solve absolute value equations. Graphing the Absolute Value Function. Applied problems, such as ranges of possible values, can also be solved using the absolute value function. In analytic geometry , an asymptote ( / ˈ æ s ɪ m p t oʊ t / ) of a curve is a line such that the distance … Lesson 6 Families of Functions. The absolute value parent function, written as f (x) = | x |, is defined as . We will also formally define a function and discuss graph functions and combining functions. The vertex of the graph of g is ()hk, . x = 0 and y = 4. Solve for x: |4 x– 2| = 8. Example: | 2x + 6 | - 3 = 13. Evaluate Piecewise Functions and Graph AV Worksheet Key. Let Ms. Rhoads know if you have any questions!! Now you're taking the absolute value of something (x - 6) times a negative. The graph of the absolute value function f (x) = | x| is similar to the graph of f (x) = x except that the "negative" half of the graph is reflected over the x -axis. As we investigate what happens for an equation with an absolute value part, we find that the graph for these kinds of equations is … Algebra 2 -25 - Functions, Equations, and Graphs WARM UP Solve each equation for y. Practice!! 1.1 I can write a function given a real world situation and write an appropriate domain and range. 2) Split into two separate equations, setting one to the negative and one to the positive. The absolute value function is commonly used to measure distances between points. Class Notes. An absolute value function is a function that contains an algebraic expression within absolute value symbols. f (x) = {x if x > 0 0 if x = 0 − x if x < 0. Here’s an example of writing an absolute value function from a graph: The absolute value function that represents this situation is where is your altitude above or below sea level before diving. Here is the graph of f (x) = | x|: f (x) = | x|. Solution : Write the given absolute value function in the form . Class Notes . 1.2 I can identify intercepts and the slope of a linear equation. The graph of such absolute value functions generally takes the shape of a V, or an up-side-down V. Notice that the graph is symmetric about the y-axis. y - h = |x - h| That is, y = -|x| + 4. Graph Piecewise Functions … You move away all other numbers by doing the opposite operation:** y - 4 = -|x| To get the vertex, equate x and (y - 4) to zero. 1.2 I can identify increasing, decreasing, and Piecewise Functions Notes. Check the solution. Textbook (Notes and Examples) Pages 370 - 372 Notes and Example 1 (Use Method 2 to sketch the graph of the absolute value of a linear function.) Lesson 2.5 Absolute Value Equations and Functions 2014. Lesson 2.5 Absolute Value Transformations 2014. Because absolute value doesn't care about the sign, you can effectively just remove the negative on the 1/2. Library of parent functions •Linear f(x)=ax+b •Constant f(x)=c •Identity f(x)=x •Quadratic f(x)=x 2 •Square root f(x)=√x •Cubic f(x)=x 3 •Absolute value f(x)=|x| •Reciprocal f(x)=1/x Draw graphs of each of these functions using symmetries, intercepts, and table of values you learned. Two methods are given for graphing absolute value functions. Therefore, the vertex is (0, 4) x = 0 and y - 4 = 0 . Follow along as this tutorial shows you how to identify the necessary parts of the equation and use them to graph the absolute value equation. Class Notes. In these notes we will Learn a new technique for graphing a function — shifting it up, down, left, right ... let's graph the absolute value "parent function", y = I x Use your calculator to graph this function in Y: What is the vertex of the graph? Exploration-of-Iransfnrmations — Vertical Shifts I. Graph y = IXI + 2 on your calculator in Y2. By graphing this function, you can see that the vertex occurs at the point (90, 0). Now, we want to give you your first taste of something that is NOT linear. The domain of f ()xx= is all real numbers. These are true statements. y = -|x| + 4. The graph looks like a "V", with its vertex at (0, 0). 2014. View NOTES GRAPHING ABSOLUTE VALUES FUNCTIONS.pdf from MATH 22 at Santaluces Community High. As f ( ) xx= is ( ) xx= is ( ) xx= is all real numbers:. Situation and write an appropriate domain and range in interval notation when given a real situation! Has a corner point at which the graph changes direction V '', with its vertex at (,... 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