Complete a function table absolute value functions

Learning Objectives Correctly substitute given input values (x) into an absolute value function. Evaluate expressions within absolute value bars following the order of operations. Apply the definition of absolute value to find the principal value of an expression. Calculate the final output value (y or f(x)) for functions involving transformations (stretches, shifts, reflections). Systematically organize input-output pairs in a function table for a given absolute value function. If you walk 5 steps forward and then 5 steps back, how far are you from your starting point? 🤔 Absolute value helps us think about distance, regardless of direction! In this tutorial, you will learn the step-by-step process for completing a function table for absolute value functions. This skill is f...

TermDefinitionExample Function TableA table that organizes the inputs (x-values) and their corresponding outputs (y-values or f(x)-values) for a given function.For f(x) = x + 1, a function table might have columns for x and f(x), with rows for x=-1 (f(x)=0), x=0 (f(x)=1), and x=1 (f(x)=2). Absolute ValueThe distance of a number from zero on the number line. The absolute value is always non-negative.|-5| = 5, because -5 is 5 units away from 0. Also, |5| = 5. Input (x-value)The value that is substituted into a function to determine the output. It is the independent variable.In the function f(x) = |x - 3|, if we choose an input of x = 1, we substitute 1 for x. Output (y-value or f(x))The resulting value after an input has been processed by the function. It is the dependent variable.For the f...

Definition of Absolute Value |x| = \begin{cases} x, & \text{if } x \geq 0 \\ -x, & \text{if } x < 0 \end{cases} Use this rule to evaluate the absolute value of any number or expression. If the value inside the bars is zero or positive, the result is the value itself. If the value inside is negative, the result is its opposite (making it positive). Transformed Absolute Value Function f(x) = a|x - h| + k This is the general form of an absolute value function. When completing a table, always follow the order of operations: 1. Evaluate the expression inside the absolute value bars (x - h). 2. Take the absolute value of the result. 3. Multiply by 'a'. 4. Add 'k'.