A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 5 years ago

How do you graph f(x)=(x+4)/(x-1)?

  • This Question is Closed
  1. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    f(x) is like y so you put in (x+4)/(x-1) in the graphing calculator

  2. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    or it would be x-4 into the calculator because x/x = x and 4/-1 = -4

  3. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    How do you graph it without a calculator though?

  4. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    -4 would be the y intercept and x would be the slope which is 1/1

  5. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    The best way to graph these functions is to first find your intercepts and asymptotes. You find the x-intercept when you let y = 0, so the x-intercept is (-4, 0). You find the y-intercept when you let x = 0, so the y-intercept is (0, -4). Plot these two points on the xy-plane. To find vertical asymptotes, set the denominator x - 1 = 0 -> x = 1. Draw a vertical dotted line at x = 1 to show that the graph CANNOT CROSS this line. To find horizontal asymptotes, check the degrees (the highest exponent) of the numerator and the denominator. Since the degrees of the numerator and denominator are both 1, you must take a ratio of the coefficients of the leading terms (the terms in the numerator and denominator with the greatest exponents). This ratio is 1, so y = 1 is your horizontal asymptote. Draw a dotted line on y = 1. Then, connect the dots (-4, 0) and (0, -4) with a nice smooth curve, but have it go past both points to "hug" the asymptotes without crossing them. Then, put another "wing" in the upper right box created by the asymptotes.

  6. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Thank you so much! That makes sense. I should probably ask this in a different question, but here it is anyways: How would I graph 5/(x+1)(x-3)? Since there's no x in the numerator?

  7. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Think about it using the methods described above. For y-intercepts, let x = 0 to get 5/(1*-3) = -5/3... (0, -5/3) is your y-intercept. If you tried to find an x-intercept by letting y =0, you would just get a false statement 0 = 5, so there's no x-intercept. The vertical asymptotes are where the denominator (x+1)(x - 3) = 0, so at x = -1 and at x = 3. For horizontal asymptotes, if the degree of the denominator is greater than the degree of the numerator (in this case, the numerator has a degree of 0 and the denominator has a degree of 2), then the horizontal asymptote is at y = 0. This should somewhat make sense being that we don't have an x-intercept. Because we're dealing with a couple asymptotes, we should get in the habit of checking intervals. What you do is pick an x value in each "yard" created by the asymptotes and see if the "wing" is positive or negative. When we choose a value in the x < -1 yard, the y-value is positive, so we draw a wing above the x-axis following the asymptotes. When we choose a value in the -1 < x < 3 yard, the y-value is negative, so we draw a parabola-looking think below the x-axis following the asymptotes. When we choose a value in the x > 3 yard, the y-value is positive, so the wing is above the x-axis.

  8. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.