Intro to absolute value texas instruments calculators. Use the definition of the absolute value function to show that f x i x is an even function. The absolute value of a number is the number of units it is from 0 on the. The standard form of an absolute value function is nearly identical to that of a quadratic function. The graph of the absolute value parent function is composed of two linear pieces joined together at a common. All of the graphs yvalues will be positive or zero. Next, a table of values is made and the absolute value function is grap. Notice, on the number line shown in figure 1, that two different numbers are 3 units away from zero, namely, 3 and 3. Perfect for acing essays, tests, and quizzes, as well as for writing lesson plans.
A step function is discontinuous cannot draw a step function without removing your pencil from your paper. Be reminded what absolute value means discover the shape of an absolute value function discover the effec. In your own words, write the meaning of each vocabulary term. To this point weve only worked problems that have linear terms in the absolute value bars. Absolute value means to remove any negative sign in front of a number, and to think of all numbers as positives or zero 2. The absolute value function, and its properties tamu math.
This 2day lesson includes 4 pages of guided notes and 2 onepage assignments. Identify what the isolated absolute value is set equal to a. What is the shape of the graph of absolute value function. This function is kind of the opposite of the first function above, because there is a minus on the absolute value expression on the righthand side of the equation. Absolute value function graph transformations notes, charts, and quiz i have. To graph an absolute value function, choose several values of x and find some ordered pairs.
Because of this minus, the positive values provided by the absolute value bars will all be switched to negative values. Absolute value equations and inequalities absolute value definition the absolute value of x, is defined as. In 5 above, because 18 is not absoluteno barsthe answer is negative. The absolute value of any number is always zero or a positive value. Numbers to the right of 0 are positive or 0 and numbers to the left of 0 are negative or absolute value. If youre seeing this message, it means were having trouble loading external resources on our website. The absolute value function is commonly thought of as providing the distance the number is from zero on a number line. Greater than or statements and less than and statements. The absolute value of a number is the distance between 0 and the number on a number line. Absolute value equations the equation x 3 is translated as x is 3 units from zero on the number line. In the case the quantities inside the absolute value were the same number but opposite signs.
Key features abs val functions day 2 textbook chapter 2. The notes begin by defining the absolute value notation and working a few examples as a reminder. Graphing absolute value functions video khan academy. Absolute value functions in order to graph an absolute value function, you will be using many of the same methods you did for quadratics. I will select x values, and students will use the definition of absolute value to determine the output values for the function. An absolute value function is a function that contains an algebraic expression within absolute value symbols. For any two real numbers x and y, we have jxyj jxjjyj. Describe the transformations to the absolute value graph when the function is changed to the following. Today you will look at key features of absolute value graphs such as domain and range, maxmin, increasingdecreasing, intercepts, and end behavior. Step functions a step function or staircase function is a piecewise function containing all constant pieces. Learn exactly what happened in this chapter, scene, or section of absolute value and what it means.
They are the same distance from 0 on the number line, but in opposite directions. Absolute value function graph transformations notes, charts. Recall that in its basic form latex\displaystylef\leftx\rightxlatex, the absolute value function, is one of our toolkit functions. All an absolute value inequality does is talk about the distance away from zero so when working with these inequalities you have two. Students learn about absolute value functions in the order below. Even though the numbers 5 and 5 are different, they do have something in common.
This is a doublesided worksheet over the absolute value function with notes and examples on one side and practice on the other. Learn how to think about absolute value as distance from zero, and practice finding absolute values. In this case we have a quadratic in the absolute value bars. Key concept general form of the absolute value function problem 1 analyzing the graph of f x. Defining an absolute value function as a piecewise function. Integers, opposites, absolute value representations using integers. The graph of the solution set is shown in figure 6. Because of this, absolutevalue functions have graphs which make sharp turns where the graph would otherwise have. One of the most used functions in mathematics is the absolute value function. Remember that distance is always a positive quantity or zero. Because the answer to an absolute expression is never negative, we then must realize that each unknown absolute value has the possibility of coming from either a positive or a negative value, producing. Its definition and some of its properties are given below. Here you will find hundreds of lessons, a community of teachers for support, and materials that are always up to date with the latest standards. Eighth grade lesson graphing absolute value functions day 1.
The absolute value parent function, written as f x x, is defined as. Two vertical bars are used to represent absolute value. Observe that this solution set consists of all x that are within 4 units of 3 on a number line figure e. Therefore, the absolute value of any number is always greater than a negative value. The following properties of the absolute value function need to be memorized. Real numbers we can represent the real numbers by the set of points on a line. Situation integer situation integer the loss of 5 yards 5 a gain of 45 yards 19 degrees below zero 19 12 degrees above zero a profit of 400 dollars 400 a loss of 29 dollars a debt of 250 dollars 250 a surplus of 25 computers. One of the four possible cases is checked as follows. Algebra absolute value equations pauls online math notes. Today you will look at key features of absolute value graphs such. Recall that the absolute value of a number is its distance from 0 on the number line. It discusses the meaning of absolute value and the notation associated with it.
The constant pieces are observed across the adjacent intervals of the function, as they change value from one interval to the next. Absolute value which can be written in interval notation as. Absolute value means to remove any negative sign in front of a number, and to think of all numbers as positives or zero. We will start the next section of class by graphing the parent absolute value function. However, upon taking the absolute value we got the same number and so \x \frac43\ is a solution. Steps for solving absolute value inequalities h 25 everett community college tutoring center there are two types of absolute value inequalities. Equation open vertex initial point shift horizonalvertical vertical change 1 yx. The vertical stretch or compression factor is 0a 0, the vertex is located at h, k, and the axis of symmetry is the line x h. An axis of symmetry of the graph of a function is a vertical line that divides the graph into mirror images.
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