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(a) determine the domain, (b) sketch the graph and (c) determine the range of the function defined by the given equation.$f(x)=|x|$

(a) $-\infty<x<\infty$(b)(c) $y \geq 0$

Algebra

Chapter 1

Functions and their Applications

Section 2

Basic Notions of Functions

Functions

Oregon State University

Harvey Mudd College

University of Michigan - Ann Arbor

Lectures

01:43

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x^2. The output of a function f corresponding to an input x is denoted by f(x).

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(a) determine the domain, …

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for this problem. We've been given a function f of X equals the absolute value of X. We're going to find three things for this function. We want to find the domain, the range, and then we're going to graph the function. Kind of. It's a visual confirmation that we have the correct domain and range for our function here. Okay, Domain, First domain are your inputs so that they're the X values that you can put into your function. Well, I'm taking the absolute value of X. Are there any numbers that I can't put into this function and taken absolute value off? Well, no. I could take an absolute value of any real number I want It could be positive. Negative zero a fraction? It doesn't matter. I confined the absolute value. So to my domain is all riel numbers. That means exes. Any number between negative infinity and positive infinity. And if you want to write this an interval notation, we can write it like that. Okay, Now range absolute value functions Always. You could think it strips away a negative science. If you put in a negative, you get out of positive. If you put in a positive. You get out of positive. The smallest number I could possibly get out of this is zero. Because absolute value of zero is zero Any other number, the absolute value is bigger. So why is gonna have to be greater than or equal to zero? I can never get a negative number out of an absolute value equation. So my domain, my exes, are all real numbers, my wise. My range is from zero to infinity. So let's graph this if x zero, why is zero right there at the origin? Let's plug in a few exes and see what we get for our wise. And that will help us graph this if I let X equal to or why will also be, too. What if I let x equal negative too well, that gives me a positive Tua's. Well, how about four? If X is four, why is four if X is negative? Four. Why is also positive, for I'm gonna be perfectly symmetrical and it comes toe a point. It's a nice straight line on one side, straight line on the other. We get this lovely V. That's my absolute value graph. That's typical absolute value graphs have that V shape to them either, pointing upward of pointing downward. So this is the sketch of my function. F of X equals the absolute value of X.

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