Find the domain and range of the function, and b) sketch a comprehensive graph of the function clearly indicating any intercepts or asymptotes.$$f(x)=rac{1}{x}-4$$...

Domain and Range from a Graph A function $f$ is given. (a) Sketch a graph of $f .$ (b) Use the graph to find the domain and range of $f .$
$f(x)=4-2 x, \quad 1< x< 4$

Hello, everyone. We're going to blow the function and which function is given and it's the mean is given and we will be finding its crew responding Range. So given funkiness therefore fix equal to X square minus one, as you can see that the highest degree is too. So this is a quadratic equation, and the Dominion give anus extra is greater than or equal to negative three and smaller than an equal to three. So this is the new me. No, this is an equation off parabola. So it is going to be something like this. Make it one this point and we confined there it intersects. The XX is by putting like we can find the X intercept in. Why intercept but F f X equal to zero, for example. So we can find X equal to bless minus one that is here and here. And if we put X equal to zero, it'll fix equal to negative one. This is this point. So we found these points. So let's plot a parable about joining these points here and here. Let's mention the range you This is negative. One negative too negative. Three, 23 two We can extend it. It's a very drove sketch, but let's just Well, just try to okay, this one. Now we want to find the maximum possible value off effects and minimum possible value up F or fix. As you can see that the menu impossible value over for fixes. This that is minus one. And the maximum possible value is on these buttons. So we can put, um, we can find off X equaled every three f off negative three. That should be cool, too. Eight. So the Dominus negative. Three, 23 and Rangers. And then you do one to eight. Uh, this is square. Break it because this is included. And that's it. You know, everyone in this re do we have to plot a function by using a graphing calculator graphing calculator. And then we have to find the range and domain off that function. The function that we have to clock a cz x squared plus four x plus three. So, first of all, let us plotted using graphing calculator X squared bliss for eggs plus three. So you can see here it's been blotted. Now we have to find the domain and range off this So first of all, what is Do me do meanness all possible. They'll use off eggs for rich. The function is defined all the news off eggs, eggs for bridge If your fix is defined so this function here is defined for all then who's off X? So our domain iss demeanors from negative infinity to infinity. Now the finding range. We can use the the graft that we have plotted. So let's zoom in on that bear. So here you can see that the minimum value that we're getting forever fix is negative one and it is going to positive infinity years. It's a parable and it's going up upto positive infinity so we can drive down the range and dream job The old responding well, youse off fo fix So Regis, Then use off fo fix four x in dummy. So here we have seen that ranges the negative one is included and two positive infinity This is the range

You know everyone in this re do we have to plot a function by using a graphing calculator graphing calculator, and then we have to find the range and domain off that function. The function that we have to plot is X squared plus four x plus three. So first of all that it's plotted using graphing calculator ex clear bliss for eggs poplars. So you can see here it's been plotted. Now we have to find the do mean and range off this. So first of all, what is do me do meanness all possible. They'll use off eggs for rich. The function is defined all the news off eggs, ex whore bitch and for fix is defined. So this function here is defined for all. Then use affects. So our domain is demeanors from negative infinity to infinity. Now, to find the range, we can use the the graft that we have plotted. So let's zoom in on that bear. So here you can see that the minimum value that we're getting for ever fix is negative one, and it is going to positive infinity years. It's a parable, and it's going up upto positive infinity. So we can drive down the range and dream job The old responding values off every fix. So Regis then use off fo fix four x into me. So here we have seen the ranges, the negative one is included and two positive infinity, This is the range

This question were asked to graph the function F of X equals four and then to state the domain in the range of the function. Of course, F of X is just another way for us to write. Why? So essentially the function that we're trying to graph is why equals for this is a constant function. If we were to try to generate values, that would go on this graph, of course, there is no value for X meaning X can be anything when x zero. Why is for when X is one? Why is for when X is negative? One? Why is for it really? Doesn't matter what value we pick for X because this is a constant function. Why is always equal to four? So remember that kind of a graph is going to be one that looks like this. Here's 1234 and why is always going to equal for regardless of the value for X. So we get a function something like this note again, if you were to try to plot these points, you'd have zero for 14243444 unaided went for it. Have the same horizontal line all the way across. So we've got our line there now. Can we state what the domain and the range would be? Remember that the domain is all the values that X takes on. In this case, there's no restriction on X X can go and be anything. And we're not really concerned about the value, anything being thrown out of possibilities. So we would say that X is all real numbers, that the domain basically encompasses any value from negative infinity to infinity. It's unbounded. You could have any value for X. The range, on the other hand, is bounded. The range has on Lee one outcome because the ranger first to wonder the Y values in this case, the Y value is always the same the Y value is for so the range, then, is the set such that why is equal before and so the range is simply all values that why takes on and that in this case is only one value for

Hi, everyone. So today we have to graft this floor step function. Okay, I pulled up the graph and I had to draw on the circles because this does not show the circles this graphing calculator. So now that we have graft it, we need to fund the Delaine and the range. Well, the domain is just negative. Infinity, infinity and the range is all whole numbers, so Oh! Oh, numbers.