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In $7-10,$ the domain of each function is the set of real numbers. a. Sketch the graph of each function. b. What is the range of each function?$$y=|x-1|$$

a) see graphb) $[0,+\infty)$

Algebra

Chapter 4

RELATIONS AND FUNCTIONS

Section 4

Absolute Value Functions

An Introduction to Geometry

Functions

Linear Functions

Polynomials

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Lectures

01:32

In mathematics, the absolu…

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In $7-10,$ the domain of e…

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Graph. Find the domain and…

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Graph each function. Ident…

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Graph each function. State…

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Find the domain and range …

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I want to look at the graph of y equals absolute value of X minus one. So this is a horizontal shift because minus one is inside the absolute value with the X coordinate, which means it is a shift along the X axis. And if x was positive one, we would get zero. So that means that this is a shift to the right one. And if I was to graft that I would start at 10 again. If I used one for X, why would equal zero? And then this is a positive, absolute value graph and we don't have a change in slope. It is a slope of one. So I could continue graphing this by going through the diagonals because that is a positive slope of one. This is a negative slope of one. But if we looked at the absolute value of negative ones, positive one. So this is our absolute value graph of X minus one. If I know that the domain is X for every, um, all real numbers for X. What are our Y values? Well, you can see that this graph does not go below the X axis. So our range is gonna be all Why values such that why is greater than or equal to zero

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