Writing absolute value equations given a graph

Sometimes, the best explanations are through examples. No, that's not right again. Horizontal changes are the inverse of what they appear to be so instead of multiplying every x-coordinate by two, the translation is to "divide every x-coordinate by two" while leaving the y-coordinates unchanged.

Always get rid of the constant first and then any coefficients last. It discusses the meaning of absolute value and the notation associated with it.

The 3 is not grouped with the x, so it is a vertical scaling. Welcome to She Loves Math.

Algebra Examples

Graph an absolute value function. An absolute value equation is an equation in which the unknown variable appears in absolute value bars.

We can find the vertex at a glance, we know which way the graph points, and we can use symmetry to find two points for the effort of finding one. Since it is added to the x, rather than multiplied by the x, it is a shift and not a scale.

Plot the points on the xy-plane and connect the dots with a straight edge. Go ahead, try another one.

How to Write an Absolute-Value Equation That Has Given Solutions

We could go on forever, so as you can see there are many many solutions to this inequality. The first operation we did was multiply by 3 and there was no problem. To review how to obtain equations from linear graphs, see Obtaining the Equations of a Line, and from quadratics, see Finding a Quadratic Equation from Points or a Graph.

Like play a smashing song on their lutes. The 2 is grouped with the x, so it is a horizontal scaling. Equation 2 is the correct one. Again, the best way to illustrate this simple idea is through the use of examples. However, due to imprecision in manufacturing, the actual values of these parameters vary somewhat from piece to piece, even when they are supposed to be the same.

Working with Fractions Now are you ready for a few on your own. If you already know the solution, you can tell immediately whether the number inside the absolute value brackets is positive or negative, and you can drop the absolute value brackets.

Students may forget to switch the direction of the inequality symbol aka "flip" the inequality symbol when multiplying or dividing by a negative number when solving. This time let's start with finding the solution symbolically and check our solution using the graph.

See if we get an answer that matches the answer we got using the graph. So which is correct.

Absolute Value Equation Calculator

The advantage of the algebraic approach is it yields solutions that may be difficult to read from the graph. Writing a Piecewise Function when it's Graph is given; Writing a Piecewise Function when It's Graph is Given. Write the piecewise functions for the graph shown.

Solution: Step 1: Locate the break point. Here it is at x = 2. Step 2: Find the equation of the graph to the left of break point.

Solve an absolute value equation using the following steps: Get the absolve value expression by itself. Set up two equations and solve them separately. Algebra Examples. Step-by-Step Examples. Algebra. Absolute Value Expressions and Equations. Write the Absolute Value as Piecewise.

The piecewise polynomials are when and when. Remove parentheses. Solve for when. Tap for more steps Subtract from both sides of the inequality.

How to find an equation given the absolute value graph?

5 - Shifting, Reflecting, and Stretching Graphs

Ask Question. -4 right? and i have another question does this apply to any if given graph and asked to find the equation if it is greatest equation graph?

Writing an equation for a log function given the graph. 5. How to graph this sin equation? 0. I also attached the notes I give my students when we first look at the writing the equation of an absolute value function graph.

Piecewise Functions

The lesson went well--my students typically find it "easy" and nice break. Find equations of lines that are parallel or perpendicular to a given line. Graph an absolute value function. Writing Equations of Linear Functions.

Graphs of linear functions may be transformed by shifting the graph up, down, left, or right as well as using stretches, compressions, and reflections.

Solving absolute value equations and inequalities Writing absolute value equations given a graph
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Absolute Value Equations on a Number Line