Absolute Value Introduction Absolute value functions come up quite often because we deal with sitautions where we cannot have a negative output. Before we begin discussing absolute value functions, let's define what is meant by the absolute value. Defining Absolute Value One way of describing the absolute value is as the distance a real number is from 0 on a number line. Another way of defining absolute value is using exponents:
What should I know about functions involving absolute values, before I start working on a problem? Absolute Values Taking the absolute value of a number or quantity is a mathematical function that describes how far the quantity is from zero on the number line.
When we evaluate absolute values, we simplify everything inside the absolute value bars, then we make the result a positive number. The point of the V is called the vertex of the function. We have a general equation that describes the vertex as at the point h, k.
The values of h and k depend upon the translations performed on the original function. We can translate our graphs vertically up and downhorizontally left and rightor both, through addition or subtraction. To translate an absolute value function up or down, you add a number after the absolute value bars.
If the number you add is positive, the graph will slide up. If the number you add is negative, then the graph will slide down.
We use the letter k to stand in for the vertical translation in our general equation. The value of k is also the y-value of the vertex. We use the letter h to stand in for the horizontal translation in our general equation.
The value of h is also the x-value of the vertex. When finding the value of h, you need to use the opposite of the sign used inside the absolute value bars. Whenever you find yourself unsure of the real value of h, you can find the right number by setting everything between the absolute value bars equal to zero, then solving for the variable.
This is another way to find h, since h is the x-value of the vertex. We can solve the above example in the way just described, if the value of h is not easily identified.
We can write a general equation for this situation by combining the two rules we had before: The easiest way to graph an absolute value function is to find the vertex h, kthen to make a chart of x- and y-values.
You can determine the x-values to put into your chart by adding -2, -1, 1, and 2 to h.
|Graphing Absolute Value Equations Worksheets||Questions Eliciting Thinking Can you reread the first sentence of the second problem? A difference is described between two values.|
Determine the values of h and k, then plot your vertex.Get the free "Absolute value equations calculator" widget for your website, blog, Wordpress, Blogger, or iGoogle. Find more Mathematics widgets in Wolfram|Alpha. While absolute-value graphs tend to look like the one above, with an "elbow" in the middle, this is not always the case.
However, if you see a graph with an elbow like this, you should expect that the equation is probably an absolute value. By using this absolute value equations calculator, you will find it extremely easy to manage things like trigonometric functions, exponents, matrices and boundaries, and other types of algebraic problems.
The feature of graph interface is also quite useful and allows you to visualize functions and calculate the gradients and do much more. Ask the student to solve the second equation and interpret the solutions in the context of the problem.
Ask the student to identify and write as many equivalent forms of the equation as possible. Then have the student solve each equation to show that they are equivalent. Consider implementing MFAS task Writing Absolute Value Inequalities (A .
Sep 02, · writing absolute value equations from graphs. Skip navigation How to Write Equation of Logarithmic Function From Graph MHF4U Pre Calculus Graph Absolute Value Equations 3 - . How To: Graph the absolute value of a function How To: Write and graph an equation in slope intercept form How To: Find points of intersection in different equations.