# graphing absolute value functions notes

These are true statements. The absolute value parent function, written as f (x) = | x |, is defined as . 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.) Solve for x: |4 x– 2| = 8. Lesson 2.5 Absolute Value Transformations 2014. 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 Let Ms. Rhoads know if you have any questions!! Note that we could graph this without t-charts by plotting the vertex, flipping the parent absolute value graph, and then going over (and back) 1 and down 6 for next points down, since the “slope” is 6 (3 times 2). Graph Piecewise Functions (4.4 YL) Worksheet Key. 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. guided notes. 2014 Absolute Value Test Review. The graph looks like a "V", with its vertex at (0, 0). Exploration-of-Iransfnrmations — Vertical Shifts I. Graph y = IXI + 2 on your calculator in Y2. Practice!! 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. This page explains how to keep track of the "V" in the absolute-value graph, and how to draw the correct shape for the quadratic equation's parabola. Solution : Write the given absolute value function in the form . By graphing this function, you can see that the vertex occurs at the point (90, 0). NOTES and EXAMPLES We’ve focused our attention this year on working with linear equations. We will also formally define a function and discuss graph functions and combining functions. As we investigate what happens for an equation with an absolute value part, we find that the graph for these kinds of equations is … 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. The range is y ≥ 0. Now you're taking the absolute value of something (x - 6) times a negative. Constant of Variation - k, where k = y/x GRAPHS OF DIRECT VARIATIONS 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. 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 … The vertex of the graph of f ()xx= is ()0, 0 . An absolute value function is a function that contains an algebraic expression within absolute value symbols. Pages 372 - … Here is the graph of f (x) = | x|: f (x) = | x|. Determine the vertex, domain, and range. Graph using a table. Please begin working on your practice: for each label whether it is a piecewise, absolute value, or step function. 1.1 I can write a function given a real world situation and write an appropriate domain and range. Recall that the absolute value of a number is its distance from 0 on the number line. Class Notes . The absolute value function is commonly used to measure distances between points. Therefore, the vertex is (0, 4) Class Notes. 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. Class Notes. Lesson 6 Families of Functions. Applied problems, such as ranges of possible values, can also be solved using the absolute value function. Then graph and find the values asked. 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? y - 4 = -|x| To get the vertex, equate x and (y - 4) to zero. Absolute Value Functions and Equations 1.1 I can write domain and range in interval notation when given a graph or an equation. Graph Absolute Value Equations Notes. In class, we use Method #2 particularly when f(x) is a quadratic function. 1.2 I can identify increasing, decreasing, and The vertex of the graph of g is ()hk, . Then check your the point where the graph changes direction. Here’s an example of writing an absolute value function from a graph: y = | (-1/2) (x - 6)| - 10. Example 2. This translates to “4 x– 2 is 8 units from zero on the number line” (see Figure 2). The graph of the absolute value parent function is composed of two linear "pieces" joined together at a common vertex (the origin). The domain of f ()xx= is all real numbers. 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. Subtract 4 from each side. 2014. x = 0 and y = 4. Highlights common student mistakes and points out how to … 2) Split into two separate equations, setting one to the negative and one to the positive. Example 1. Piecewise Functions Notes. y = -|x| + 4. 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. A curve intersecting an asymptote infinitely many times. 1) Isolate the absolute value. 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. The absolute value function that represents this situation is where is your altitude above or below sea level before diving. 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. The graph of the absolute value function resembles a letter V. It has a corner point at which the graph changes direction. Graphing Linear Equations ⃣Create appropriate axes with labels and scales with given information ⃣Draw a graph of an equation 2.3 2.4 Piecewise Functions ⃣Graph piecewise functions ⃣Write equations of piecewise functions CB 2.4 Absolute Value Functions and Step Functions ⃣Graph absolute value and step functions 2.7 Transformations of ⃣ Now, we want to give you your first taste of something that is NOT linear. Worksheet to accompany part 1. In this chapter we’ll look at two very important topics in an Algebra class. You move away all other numbers by doing the opposite operation:** Because absolute value doesn't care about the sign, you can effectively just remove the negative on the 1/2. Now that the equation has been simplified to y = |1/2 (x - 6)| - 10, you can get to graphing. Evaluate Piecewise Functions and Graph AV Worksheet Key. Example: | 2x + 6 | - 3 = 13. 2 NOTES Graphing Absolute Value MB.notebook May 05, 2020 Graphing Absolute Value Functions “Parent Graph” Domain _____ Range _____ x y Transforming an Absolute Value Graph: k represents a vertical shift up or down + k means a vertical shift up k units Graph Absolute Value Equations Worksheet Key. Graph Piecewise Functions … Lesson 2.5 Absolute Value Equations and Functions 2014. 1.2 I can identify intercepts and the slope of a linear equation. The solution set of the equation | x| = 3 is {3, –3}, because |3| = 3 and |–3| = 3. Lesson 7 Two-Variable Inequalities. Graph the absolute value function given below. View NOTES GRAPHING ABSOLUTE VALUES FUNCTIONS.pdf from MATH 22 at Santaluces Community High. Graphing the Absolute Value Function. Title: Piecewise, Absolute Value, and Step Functions In analytic geometry , an asymptote ( / ˈ æ s ɪ m p t oʊ t / ) of a curve is a line such that the distance … x = 0 and y - 4 = 0 . Resistance of a Resistor. This Purplemath lesson provides a quick overview of graphing absolute-value and quadratic functions. Its slope is m = 1 on the right side of the vertex, and m = - 1 on the left side of the vertex. 2014 A Review Solutions . How to solve absolute value equations. Electrical parts, such as resistors and capacitors, come with specified … f (x) = {x if x > 0 0 if x = 0 − x if x < 0. Algebra 2 -25 - Functions, Equations, and Graphs WARM UP Solve each equation for y. Absolute value. Class Notes. Check the solution. 1) Isolate the absolute value: ** The steps are the same as if you were getting the x by itself.

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