Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

The absolute value function is defined as follows: $y=|x|=\left\{\begin{array}{ll}-x & x<0 \\ x & x \geq 0\end{array}\right.$ Sketch the graph of $y=|x|$.

Algebra

Chapter 1

Functions and their Applications

Section 2

Basic Notions of Functions

Functions

Campbell University

Oregon State University

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).

03:18

02:49

Definition of absolute val…

02:28

Absolute value graph Use t…

01:39

Absolute value functions G…

01:25

The absolute value functio…

01:23

00:47

How can you use the graph …

00:35

01:18

The piecewise-defined func…

for this problem, we're going to sketch the graph of the absolute value function. Why equals the absolute value of X? Now we can think of the absolute value as a piece wise function. If X is, we're gonna break into two pieces. X is less than zero or X is greater than or equal to zero. Let's do the second case first. If X is positive, then the absolute value makes no difference. The absolute value of a positive number is just itself. Absolute value of zero is just itself is just zero. The only time the absolute value changes things is if it's a negative number. So the absolute value of a negative number is going to be the opposite of the number. So the absolute value of negative three is the opposite of negative three or positive three. So there is our, um, piece wise function to graph this. Let's take each of them separately. If I have the first piece, Why equals negative X? Well, if you think about slope intercept form, which is why equals M X plus B. This has a B of zero, so it intersects at zero and it has a slope of negative one. Now this is Onley valid for negative X is so I'm gonna be coming up this way. I connect these dots. That's what it looks like for negative exes. Now, what if excess positive? Well, then I have the line y equals X again. It has a zero of the Y intercept. 20 So again, that's what the origin. But now it has a positive slope of one, so it's going to be coming this way. So, um, absolute value graph has a very characteristic V shape, you know, it's gonna be coming on one side. It hits whatever. That that bottom point where it switches over from negative slope to a positive slope and it comes into that V. So the graph here, shown in red is the sketch of the graph of the absolute value of X

View More Answers From This Book

Find Another Textbook

Numerade Educator

02:43

A rectangular swimming pool is 30 feet by 40 feet. If a rectangular strip of…

05:16

(a) Determine the equation of the tangent line to the circle $x^{2}+y^{2}=16…

02:41

sketch the graph of the given ellipse, labeling all intercepts.$$\frac{x…

02:22

a) sketch the graph of the given function, and then draw the tangent line at…

Compute the indicated limit.$$\text { (a) } \lim _{x \rightarrow \infty}…

02:36

Sketch the graph of $\frac{(x-1)^{2}}{4}+\frac{(y+2)^{2}}{9}=1$

04:53

Determine an equation for the line (a) parallel (b) perpendicular to $2 x-5 …

03:27

Sketch the graph of $y=\operatorname{ceil}(x)+x$ for $-3 \leq x \leq 3$.

02:18

Sometimes when one plots a set of data, it appears to be piece wise linear, …

00:52

Find $f^{\prime}(x)$.(a) $f(x)=53$ (b) Give a geometric explanation for …