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Use a graphing utility to graph the rational function. Determine the domain of the function and identify any asymptotes.$$y= rac{2 x^{2}+x}{x+1}$$...

Question

Use a graphing utility to graph the rational function. Determine the domain of the function and identify any asymptotes.$$y= rac{2 x^{2}+x}{x+1}$$

Use a graphing utility to graph the rational function. Determine the domain of the function and identify any asymptotes. $$y=\frac{2 x^{2}+x}{x+1}$$



Answers

Use a graphing utility to graph the rational function. Determine the domain of the function and identify any asymptotes. $$y=\frac{2 x^{2}+x}{x+1}$$

This goes in any given that logical to expect this one. My X minus one. Nice have been peerless. See why it's not defined for exited World one. So no, it's not true. By completing the left can limit why lesson and left and limit off like extends to one minus minus infinity. So the practical lesson. Top rich. Excellent one. Now we need to find out. I learned a lesson about Auslander lesson books, which we can no like this quiet photo expert Last one x minus one And this reconnected. In other words, express one less bluepi X minus one. Now from this question the slanted icing helping Why is it working? Excuse one from the Kraft vacancy. Now what? Take a listen. Talk is acceptable one and that's Montedison Notice why vehicle to express one Even with new life and the graph the dependent by this tonight

So here we are graphing the function F of ax equals two over X plus one. So first, let's look at the graph of F of ax equals two over X. Okay, because two over acts, there's graft right here. We see that we have a vertical Assam told at Well, at X equals zero, right, Because what makes the denominator zero? Well, zero. And we also see that we have a horizontal Assam told at while y equals zero or the X axis right? Is ECUs bigger and bigger and bigger? We approach zero. We approach the X access in the positive and negative direction. Um, and what's gonna happen? We look at two over X plus one. Well, you're just a The X plus one is a horse horizontal shift, but it's a shift to the left of one unit, the opposite of whatever Sinuses have X plus one. We are shifting to the left one unit. The same graph of two over X just shifts, one units the left, and then what happens to our vertical acid tote with shifts? One year it's the left and notice that what makes the nominator zero now well X plus one is equal to zero When x It was negative. One ex cannot be negative one, and we see that negative. Want X equals negative one is the line right here. So this line and up and down by right is X equals negative. One is our vertical s in tow, and our horizontal Assam toe is still the X axis. That's not gonna change with a horizontal shift, because noticed the degree of the denominator is still won. The degree of the numerator could think of us two times zero is still zero. So if the degree of the denominator is greater than the degree of the numerator, we have a horizontal Assam tote at and why equals zero? Well, the X axis and that's not going to change. What changes from two over X to 12. Reckless one is the big lesson tote, which is now at X equals negative one. All right, so there is our graph

Okay, so here we have in the function F of X is equal to two acts provided by X minus one. So here is the graph right here. Noticed that where where is our vertical Assen tone? It's at X equals one, right? You put in one to our function. We have one minus 10 We divide by zero. So X equals one which is right here. It's when he's lying. Is 1/2 s equals one. You can see the graph is approaching that line. The top. And you go down, down, down, down We do out. We approach X equals one lips. Um, whoops. Let's go home. You know, um, another way. So are vertical. Assen tote is at X equals one and are horizontal Assam tote. Well, notice that the degree of the numerator and denominator are both one, so that the same. So our horizontal lasting coat is just the ratio of the coefficients coefficient of top is too. The court vision of the bottom is one invisible one in front of the X. So therefore are horizontal. Assam tote is at two. And we see that the top and bottom graph, um, as you get bigger and bigger. Both approach the line. Why equals two? So the line y equals to this line right here is our horizontal. That's a coat and a very pleasant Oh, is at X equals one. All right, you go. It's our graph.

Okay, so here we are. Graphing F of X is equal to well to plus ax, and that is all divided by X minus one. Who plus X over X minus one weaken. See Graph Right here. So I'm gonna get better view of it. Um, So what is our vertical Assam total? Just with the denomination. Zero vertical assam told at X equals one X equals one. Um, is what makes the denominator equal to zero. So a Virgo asking coat at X equals one. And how about a horizontal? Oh, Assam tote? Well, two plus X. Can you write that one as X plus two and again? Did you see that? The degree of the numerator is one? So is the degree of the debt of the denominator. So our horizontal asking tone is just while the racial coefficients, which is one of one, just one. So our horizontal asked him. Tote is at, um, wank was one and our or in our birth left untold Is that exit was one. All right, take your


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