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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?$$\mathrm{f}(x)=|4 x|+1$$

a) see graphb) $[1,+\infty)$

Algebra

Chapter 4

RELATIONS AND FUNCTIONS

Section 4

Absolute Value Functions

An Introduction to Geometry

Functions

Linear Functions

Polynomials

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In mathematics, the absolu…

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In $7-10,$ the domain of e…

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I want to look at the graph of y calls absolute value for X plus one and take a look at the domain and range of this graph. So, um, first of all, it's all about family of functions. We can rewrite this as a slope before of the absolute value function X plus one. So that means that we have no horizontal shift, but we do have a vertical shift. This plus one is a vertical shift, and we have a slope of four. So let me start by finding my vertex point. If there's no horizontal shift, it's going to be on the Y axis. Ah, vertical shift of plus one says my Vertex point is going to be at +01 and a slope of four. Someone go over one a 41234 to the right, 11234 And we're gonna go to the left. 11234 left 11234 You can see that it is symmetric. So our absolute value graph will look like this. And now we can see that the domain is X for all riel values of X. But when we talk about the range. The ranges are why values and you can see here that the graph does not go below y equals one. So it's all why values graven or equal to one?

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