find vert and slant asymptote *check work please

[kpx001]

y = 2x^2 - 6x -7 / (x-4)

vertical: 4 because vert based on denominator
hortizontal: none because the numerator power is higher
slant: y = 2x-2 because i divided x-4 by 2x^2 - 6x - 7
y-int: 0,7/4 because i made subbed 0 in for x

x-int= im having trouble w/ this. i got (0,(3+/- i sqroot(5))/7)

basiclly the numerator i used quadratic formula and got 6+/- sqroot -20 / 14 and kept simplifying. did i get the x-intercept correctly?

 

[galactus]

For the x intercept, solve the quadratic.

\(\displaystyle \L\\2x^{2}-6x-7=0\)

It is not complex. There are two real solutions. I see you have an 'i' in your answer.

\(\displaystyle \L\\x=\frac{\sqrt{23}+3}{2}; \;\ \frac{3-\sqrt{23}}{2}\)

Your slant asymptote has an incorrect sign. Should be y=2x+2.

Okey-doke. Otherwise, good work.

 

[tkhunny]

Before I hit you with a barage of stuff, Good Work! It looks like you are on the right path. Now, let's learn a few things...

Your notation needs a little help. Parentheses are important. Remember the Order of Operations. Your function is y = (2x^2 - 6x -7) / (x-4).

The vertical asymptote is NOT "4". You need an equation of a line. Try "x = 4".

Personally, I would avoid the terminology "slant asymptote" since that works only for degree of numerator ONE greater than degree of denominator. It's just an asymptote.

Check your long division. y = 2x+2 looks a little closer.

x-intercepts need help. First, it should be (something,0), not (0,something). Second, what's that "i" doing in there? Try that Quadratic Formula again. Something went wrong. I get \(\displaystyle (\frac{3+\sqrt{23}}{2},0)\) for one of them.

No kidding, this looks like a ton of comments, but it's just a few minor tweaks. Do NOT be discouraged.

 

[stapel]

y = 2x^2 - 6x -7 / (x-4)

vertical: 4 because vert based on denominator

I will guess that the function is meant to be (2x^2 - 6x - 7)/(x - 4), rather than 2x^2 - 6x - (7)/(x-4), as posted. Also, I will guess that the instructions were to "find the asymptotes and intercepts, if any". :idea:

If so, then your first answer, x = 4, is correct.

hortizontal: none because the numerator power is higher
slant: y = 2x-2 because i divided x-4 by 2x^2 - 6x - 7

You are correct on the horizontal-asymptote bit, but you might want to check your work on the slant-asymptote bit. When you did the graph, did you notice that your slant asymptote was, um, a bit low...?

y-int: 0,7/4 because i made subbed 0 in for x

I will guess that, rather than two numbers, you actually mean the point, (x, y) = (0, 7/4). If so, your answer is correct.

x-int= im having trouble w/ this. i got (0,(3+/- i sqroot(5))/7)

Look at your graph. If the graph crosses or touches the x-axis, then complex-valued x-intercepts cannot be correct. :shock:

Check your arithmetic inside the square root! :wink:

Eliz.