in-7-10-the-domain-of-each-function-is-the-set-of-real-numbers-a-sketch-the-graph-of-each-function-3

Question

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

Mary Brese · Accepted Answer

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&#x27;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&#x27;s no horizontal shift, it&#x27;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&#x27;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&#x27;s all why values graven or equal to one?

Mary Brese · Answer

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&#x27;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

Finian Lickona · Answer

All right, So for this exercise, we are given the function G of X equals the absolute value of three minus X over too. Minus three outside of the absolute value bars. So the first thing I&#x27;m gonna want to do Thio make the graph of this is I&#x27;m going to want to figure out what value of X makes this internal absolute value function part equal to zero. So that really amounts to solving a simple algebraic equation. Three minus x over two equal zero. So I&#x27;m gonna move this X over to the other side. We have three equals, X over two. I&#x27;m gonna multiply both sides by two. And I get that X equals six No x equal six. Okay, so I know that if I go to an ex value of six, this is going to reduce to zero. So I go over to six and that&#x27;s gonna be on the zero line, except that we also have this negative three on the outside. So that means that I&#x27;m going to have to shift down three. So this is really going to be the vertex of my absolute value function. And now to graft the rest of it. We just have to observe what the slope coefficient is on the X variable so we can rewrite this as 1/2 or negative 1/2 times x. So this means that for all X values greater than six, we&#x27;re going to have three minus. Let&#x27;s let&#x27;s pick nine, for example or no rather let&#x27;s pick eight. So if we plug in eight, we have a divided by two, which is 43 minutes for his negative one. But the absolute value that makes a positive one so positive one minus three equals negative, too. So we know that our next point is going to be right there, and because it&#x27;s an absolute value function, we know that there&#x27;s going to be a symmetry so I can graft that point right there and extend my graph like so. And of course, we can extend both of these often to infinity. It&#x27;s just not worth drawing that much, so now we want to determine the range of our function, and if we look at this, we see that the Y value goes all the way down to negative three. But it doesn&#x27;t get any lower than that. So our range is all of the Y values and greater than or equal to negative three. Yeah, I&#x27;m gonna write that a little more allegedly. Okay.

Finian Lickona · Answer

All right. So for this exercise, we are given the function why equals the absolute value of three X plus nine and were given that the domain is all real numbers and were asked to draw a graph of this function and then to determine its range. So the first thing I&#x27;m gonna do is rewrite this just as a simple linear equation. And so I see that Y equals three experts. Nine. That means that nine is going to be my y intercepts. I&#x27;m gonna grab that right there. And I said I have a slope of three. So instead of going over one up three, I&#x27;m going to go down three end over one in the negative direction. So let&#x27;s see, we&#x27;re gonna wanna go from nine down to six and over one so our next points gonna be right there. And then now we go over another one, and we&#x27;re gonna go down to three. Then we&#x27;re gonna go over another one, and we&#x27;re gonna go down to zero. I&#x27;m just gonna swear to connect those right there. Now, if I were to continue this process, I would go into the negative range of why values, But because I have this absolute value function. If I were to plug in the value negative four right here I have three times. Negative for is negative. 12 plus nine is negative. Three, but that becomes a positive three because of the absolute value bars. So for the value negative four. I&#x27;m actually gonna Grafton output of positive three. So you can see that the absolute value that slope wasn&#x27;t that great here. As you can see, the absolute value function kind of creates this V shaped reflection. And now we want to determine the range of this function, and we can see very clearly that the Y values go all the way down to zero, but they don&#x27;t go into the negative range. So the range of this function is actually all why values greater than or equal to zero.

Elizabeth Xu · Answer

two graf affects is equal to four if X is less than a negative one, and negative for Rex is great with negative one. Let&#x27;s start with the part when access does the negative, So lesson ready that center with the negative one. Here you have X equal to four. So this is included because we have less than or equal to gun when were greater than negative one. We have negative for here so far our range, because we know that why can only be in four or negative for our range is why single before or why it equal to negative for.

Tony Ni · Answer

but doing this question when I asked to drop dysfunction, Uh, we can see that there is no about you acting. Why can I goto? And some milk and Caesar? They&#x27;re both schools are negative. Go forever onwards on to put into post direction. So that means money coming. It&#x27;s going for negative. Infinity to infinity. I want my ring just went on and on.

Problem

In $7-10,$ the domain of each function is the set…

Problem 9 Easy Difficulty

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

Answer

a) see graph
b) $[1,+\infty)$

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Ann Xavier Gantert

Algebra 2 and Trigonometry

Grace H.

Catherine R.

Anna Marie V.

Alayna H.

Absolute Value - Example 1

Absolute Value - Example 2

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

Algebra 2 and Trigonometry

Grace H.

Catherine R.

Anna Marie V.

Alayna H.

Absolute Value - Example 1

Absolute Value - Example 2

Ann Xavier GantertAlgebra 2 and Trigonometry

Grace H.

Catherine R.

Anna Marie V.

Alayna H.

a) see graph
b) $[1,+\infty)$

Ann Xavier Gantert

Algebra 2 and Trigonometry