in-13-20-a-graph-each-function-b-is-the-function-a-direct-variation-c-is-the-function-one-to-one-f-2

Question

In $13-20$ : a. Graph each function. b. Is the function a direct variation? $c$ . Is the function one-to-one? 
$\frac{x}{y}=2$

Emma Chickles · Accepted Answer

and this problem were asked a graph of function given the ex otherwise equal to two. First. Let&#x27;s see you write this equation. Families playing both sides by why, on dividing both sides by two to give us a function wise equals a to X. Now we can graft this function when Mexico says zero y is equal to zero when X is equal to two, why sequels before and so on. This will give us a linear function. Now we need to determine if this function is a direct variation. The function is a direct variation when it does a linear function that is 1 to 1, as we determined in part A. This is a linear function, and that&#x27;s because the ratio between these two variables is a constant constant equal to two. So this is a direct variation. All in your functions are direct. Very are our 1 to 1. But we can also see this by using the horizontal line test. No matter where we draw a horizontal line, our graph will only intersect the horizontal blind at one point, so this function is 1 to 1

Yemi Uthman · Answer

for this question. Our function given is why over X equals two. And if you multiply X by both sides, we could change this toe y equals two x So now we can make a tip. Look, I used to find our inputs and outputs. So are inputs will be negative to negative 101 and two on our outputs will be negative for negative too. 02 and four Now I can grab these individually so have negative to negative four down here Negative one negative to over here zero comma zero over here, one comma to appear and to come before up here So now we can find our graft Look something like that. So now you can see that this is direct variation because recreation equations usually fall, the form y equals K x and we have y equals two x therefore, K equals two And if we use our vertical line and horizontal line tests will see that each vertical line we draw only passes through one point no matter where we draw it on the horizontal line only passes through one point as well, no matter where we draw it. So this is a 1 to 1 function

Yemi Uthman · Answer

our function here is why equals one half X. So the first thing we can dio is make a table of values and so have X year one half x, which is just why so the first bottle being negative for negative too. Zero two before those air inputs and outputs will be negative to negative 101 and two. So now we can graph each of these individually, so we&#x27;ll go down to negative four Common negative two will be here negative to common. Negative one will be here. 00 will be here to come. A one will be here and four comma two will be appear. So your graph looks something like that. And next you could see that this is directory ation because direct variations usually follow the form y equals K x and here we have y equals one half X. Therefore, Cajuste equals one half. Now, lastly, using our vertical line and horizontal line, tests will see that this is in fact a function and it is 1 to 1 because for our vertical line test will see that it only passed through one point no matter where we draw the vertical line and for the quarters on salon test. It also only passes through one point at each horizontal line, so this is a 1 to 1 function.

Yemi Uthman · Answer

for this question we see their function is why equals negative X. So the first thing we&#x27;re gonna do is make a table of values like negative to negative 101 and two. So outputs will be positive to positive 10 negative one and negative, too. So you can graft. These values will have negative to common to appear negative one comma 10 comma zero 11 common negative one. And to common negative, too. Sir Graph will look like this. Therefore, next we have the we can see if it&#x27;s a direct variation and recreation equation to usually follow y equals K X. So here will have y equals negative one x, So that means K equals negative one. And this is a 1 to 1 function because if we use our vertical line, tests will see that only passes through it each point. Once like that, we could go anywhere and horizontal on test shows that each horizontal line only goes through one value

Yemi Uthman · Answer

the first thing we could do for this questions create a table of values. So if our function is why equals three X, we&#x27;ll have X here three x, which equals Why here. So you can put negative too Negative. One 01 And to Sophie plugging negative to hero come out with negative six. Negative one will give us negative 30 will give 01 will give us three to will give us six. So now we comply each of these values into our table. So go negative to negative. Six be done here. Negative one negative three will be here. 00 will be here. One common three. Be right here. Two comma six will be up here secret connect the use no beer graph. So next you can see that this is a direct variation and we can see that with as direct variation question equations can hear. In this y equals K X And here we have y equals three X, Therefore, K equals three and last. We can use our vertical line test the horizontal line tests to see that this is in fact a 1 to 1 function

Emma Chickles · Answer

and this problem. We&#x27;re asked to graph the function wise equal to eight over X. First, let&#x27;s look at the domain and range of this function because X is in the denominator and order for why to be defined. X cannot be equal to zero to find the range we can think of. One X goes towards infinity. Why will start to perch zero but not reach it as X goes to negative infinity? Why will go to zero but also not reach it? So there&#x27;s an accent OK at y is equal to zero. In other words, the range of this function is the set of all real numbers, excluding zero. With that in mind, we can start to draw our graph. We know that there&#x27;s an ask himto at X equals zero and that Y equals zero. Now we can look at different points in this graph when X is equal to one. Y is equal to eight on X is equal to two. Why is equal to four and so on? Similarly, when X is equal to negative one y singleton negative eight. When X is equal to neck that to Y is equal to negative for and so on. So our graph looks like this. Now I ask to determine if this function is a direct variation in order for a function to be a direct variation and needs to be a linear function. And once one, this function is not a linear function, because the ratio between these two variables is not constant, as you can see her in the non constant slope, However, this function is 1 to 1. Because no matter where we drop any horizontal line, the graph only intersect. This was on the line in admirals one, please. So this function is 1 to 1.

Problem

Is every linear function a direct variation?

Problem 20 Medium Difficulty

In $13-20$ : a. Graph each function. b. Is the function a direct variation? $c$ . Is the function one-to-one?
$\frac{x}{y}=2$

Answer

Based on the graph above, the function is one-to-one.

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Based on the graph above, the function is one-to-one.

Algebra 2 and Trigonometry

Anna Marie V.

Heather Z.

Alayna H.

Kayleah T.

Absolute Value - Example 1

Absolute Value - Example 2

Ann Xavier GantertAlgebra 2 and Trigonometry

Anna Marie V.

Heather Z.

Alayna H.

Kayleah T.

Ann Xavier Gantert

Algebra 2 and Trigonometry