a-sketch-the-graph-of-yx-b-sketch-the-graph-of-y-x-c-describe-the-graph-of-y-x-in-terms-of-the-graph

Question

a. Sketch the graph of $y=|x| .$
b. Sketch the graph of $y=-|x| .$
c. Describe the graph of $y=-|x|$ in terms of the graph of $y=|x|$

Mary Brese · Accepted Answer

absolute value. Functions are parent function is f of X equals the absolute value of X. And that is because, um it does not have a horizontal shift, which means the Vertex starts at X equals zero. It does not have a vertical shift on the outside, which means the Y value is also zero. So this has the Vertex at 00 and the slope value is a positive one. So that means it&#x27;s going to open up and we&#x27;ll take a look at that. Well, here&#x27;s the graph of that function. Where the Vertex is at 00 to the right of the graph are absolute value. Our slope is positive. One to the left of the graph. We used the opposite slope, so that&#x27;s negative. One. How does that compare to a part of the family? Absolute value. Negative, absolute value of X. So again, there is no horizontal shift inside the absolute value bars. There&#x27;s no vertical shift to the right of the absent value bars, so the Vertex is still at 00 but we now have instead of a is equal toe. One. We now have a is equal to negative one, which means we have the opposite slope. So to the right of the Vertex, we have a negative one slope and to the left of the Vertex we have opposite of that which would be a positive one slope. So this should open down because we have the opposite slopes. So let&#x27;s take a look at it and verify that a negative sign to the left of the Absolute Value bar states that your avert your absolute value graph is going to open down. So I&#x27;ve got the absolute value of X O. But I need to go and put a negative sign in front of that. So let&#x27;s put a negative, sign him from that and see what that looks like. So it agrees with our discussion that the Vertex is still a 00 There is no horizontal, a vertical shift, and we are using the opposite slope to the right of the Vertex. Instead of a positive one soap. We have a negative one soap to the left of the Vertex. We used the opposite of the slope that you see, and so that gives us a positive. So again, a negative sign to the left of the absolute value bars. Some people will say it flips it upside down, but the proper vocabulary is the absolute value graph opens down.

Mary Brese · Answer

we&#x27;re looking at, um f of X equals absolute value of X. And when you change the equation, toe f of X equals absolute value of X Plus two or F of X equals absolute value of X minus two. Since they are all absolute value functions, we call this a family of functions. The question is, is what happens when we put a plus two after the original parent function or a minus two? So let&#x27;s take a look at some graphs. We want to look at the absolute value of the absolute value of X first. And so here&#x27;s our absolute value of X. It starts at the origin, and we have a slope of one to the right. We have a absolute value of slope of negative one to the left s. So this is your ab, your parent function of absolute value of X. But what happens if we add to to the right hand side? So we&#x27;ve got absolute value of X and on the outside, we&#x27;re going to add to, so if you&#x27;ll notice, we still have a slope of one, and we know it&#x27;s a slope of one without even looking at the grid because our blue graph are apparent, function is parallel to our new function. The only thing is the Vertex point shifted up one. So for each x value, the graph shifted up. I mean shifted up to because in our parent function, when X was one, why is also one? But now on X is one. Why is three when X is too? Why was to now exes? Four. So you can see that adding to outside the absolute value bars. We call this a vertical shift and you&#x27;re adding to toe all of the original function values. So that shifts up to what happens if we put a minus two. You probably can guess at this point let&#x27;s do the I&#x27;m suit value of X. And this time we&#x27;re going. Teoh, subtract two and you&#x27;ll see that our third function again. Our vertex point is when x zero, because that hasn&#x27;t changed. So the only thing that changed is once we found our original function value all of those values we subtracted to from all of the original by values so adding or subtracting a constant number outside of your absolute value bars is called a vertical shift So let&#x27;s go back to our equations. This is our parent function. The Vertex is at 00 and this is a vertical shift. I&#x27;m sorry. This is a vertical shift up. One are up to, and this is a vertical shift down to

Finian Lickona · Answer

All right, So in this exercise, we are asked to draw a couple of graphs and then compare the two. So the first thing we&#x27;re going to have to do is try The graph of y equals the absolute value of X. So if we were to draw that, it would look something like this. We have the equation y equals X for all positive values of X. And we have the equation. Why equals negative X for all negative values of X? So we get this kind of symmetric V about the origin. Because if we were to say plug in negative five, we get y equals the absolute value negative or let&#x27;s do negative for which is positive for so the y value would be positive for Okay, so we&#x27;re just gonna un draw that graph. And the second graf we have to sketch is the graph of y equals the absolute value of X plus two. So now this is going to look exactly like the other graph that we just drew, except that it&#x27;s going to have a shift to it. So if we were to plug in the value of negative two for X a negative to pose positive to zero. So that would be what makes y equals zero. So we have the exact same sort of V shaped with the exact same slope on either side, except it&#x27;s been shifted over to the negative to spot. And now we need to sketch the graph of why equals the absolute value of X minus two. Now, this is the exact same thing. Only instead of shifting over to the left, we&#x27;re gonna be shifting over to the right because if we plug in positive two for X, that&#x27;s what makes White with zero. So that&#x27;s that graph right there. And okay, now we need thio generally describe really to generally described the graph of y equals X plus a where a is any constant in terms of the graph of y equals x. So as we conceive from the previous example, what adding this a term does is it shifts the graph to the left or right, depending on the sign of the constant by whatever the value of A is. So if I were to say that a is equal to negative three, for example, I shift my graph so that its Vertex is real action on a equals positive three. Then I shift my graph over to the left in the negative direction because it takes a negative value to cancel out a positive value. All right, so in general, the, uh, constant is going to shift the graft to the left or the right. If it&#x27;s inside the absolute value brackets, it&#x27;s not gonna change this slope. And it&#x27;s also not going to change the vertical.

Finian Lickona · Answer

So for this exercise, we&#x27;re going to have to graft the functions. Why equals the absolute value of X Y equals two times the absolute value of X, and why equals 1/2 times the absolute value of X. Okay, so the first thing we&#x27;re gonna do is sketching the graph of y equals the absolute value of X. So that&#x27;s pretty straightforward. That is just this graph right here and then because it&#x27;s an absolute value function, all the negative X values generate positive. Weil puts. Okay, so now for this next function, what I&#x27;m gonna do is I&#x27;m gonna plug in one and negative one for the value of X and see what I get is my output. So if I plug it in one, I have two times. One is two. So that means that my output actually puts me right here by program negative one. I get two times the absolute value of negative one, which is also positive too. So I have another point right there. So the graph of y equals two times the absolute value of X actually looks. Yeah, on the 1st 1 Wasn&#x27;t that great? Try that back in real quick all right. Anyway, sorry for the terrible graft, but you get the idea. Okay? And now if I plug in, I&#x27;m gonna pick the values to And negative too, for this next function. And I&#x27;m going to write Ah, 1/2 times. The absolute value, too is one. So I&#x27;m going to go over to the X value to the Y value of one and 1/2 times. They absolutely negative too is also one. So this graph actually looks like this. All right, So now we need Thio are going to want to explore how, in general the function y equals a whereas any constant times the absolute value of exchanges. The graph of y equals the absolute value of X. So this a coefficient is basically a scaling factor. It increases the slope of the line or decreases the slope of the line based on whether or not this a value is less than greater than or equal to one. So if I were to substitute and say five for this, a value that would change this slope of my absolute value function to five. So I have to go over warning up to, like, five, which is all the way up here at anyways. So in general this a value in front of the absolute value term is going to be a scaling coefficient.

Finian Lickona · Answer

all right. So for the first part of this exercise, we need to sketch the graph of Why equals X squared. And I&#x27;ve already loaded that just for convenience. And for the second part of the question, we need to sketch the graph of y equals three x squared. So if I plug in zero for X, I get zero. That&#x27;s our first point. If I plug in one for X, I get three times one, which is going to be three. If I plug in negative one, I also get three. So that parable is going to look something like this, and there&#x27;s no curvature down there. Even though there should be. It&#x27;s just kind of hard to draw. Uh, And so, for the next part of the question, we have to sketch the graph of Y equals 1/3 x squared. So that&#x27;s gonna look something like this again. We have zero point. And then if I plug in, let&#x27;s say let&#x27;s say I plug in three for X Squared Perec&#x27;s So I get nine as X squared and 1/3 of nine ist three. So if I go over to three and I have to go up to three, and then the same thing applies for negative three. So this per Abalo looks something like this. Okay, So for the next part of the question, we have to describe the graph of why equals Yeah, why equals a X squared when a is greater than one? So when a is greater than one, the graph of y equals X squared is going to stretch The parabola of the basic graph of y equals X squared. It&#x27;s going to make it longer in skinnier. And then when a is between zero and one, then it compresses the graph. It sort of squishes it and makes it fatter. So we have, ah, bigger paro Ebola or sort of wider problem for smaller values of a between zero and one. And we have a longer, skinnier problem for values of a greater than one

Carson Merrill · Answer

So this is the graph. We would get it because, um, whenever the value of X is negative, it will cancel out with the absolute value, Um, of the X And then when this is the case, it&#x27;s almost like the function to access. We see because you have some value, some positive value of X, plus the same positive value vax. That&#x27;s why it&#x27;s two acts. So if we want to make this into a piece vice function without absolute value, we will get why equals zero, Um, from the interval, Um, where X is less than zero. Just like that is what we would get this red line right here. And then this part of the equation is going to be. Why equals two acts where X is greater than equal to zero. So we would end up getting this black line right here on, and this would be our function in a piece of ice form

Problem

a. Sketch the graph of $y=|x| .$ b. Sketch the g…

Problem 15 Hard Difficulty

a. Sketch the graph of $y=|x| .$
b. Sketch the graph of $y=-|x| .$
c. Describe the graph of $y=-|x|$ in terms of the graph of $y=|x|$

Answer

a) see graph
b) see graph
c) The graph $y=-|x|$ is the graph of $y=|x|$ reflected about the $x$ -axis.

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Ann Xavier Gantert

Algebra 2 and Trigonometry

Catherine R.

Heather Z.

Kayleah T.

Maria G.

Absolute Value - Example 1

Absolute Value - Example 2

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a) see graphb) see graphc) The graph $y=-|x|$ is the graph of $y=|x|$ reflected about the $x$ -axis.

Algebra 2 and Trigonometry

Catherine R.

Heather Z.

Kayleah T.

Maria G.

Absolute Value - Example 1

Absolute Value - Example 2

Ann Xavier GantertAlgebra 2 and Trigonometry

Catherine R.

Heather Z.

Kayleah T.

Maria G.

a) see graph
b) see graph
c) The graph $y=-|x|$ is the graph of $y=|x|$ reflected about the $x$ -axis.

Ann Xavier Gantert

Algebra 2 and Trigonometry