Calc problem

Consider the function y=(kx)/(x-k)

a. Show that y is symmetric with respect to the line y=x.
b. Write the equations of the horizontal and vertical asymptotes of y.
c. Find the point(s) of intersection of y with the line x-y=-2k, and find the slope of the tangent line at the point(s) of intersection.

Please show step-by-step work in your answers. Thanks in advance!!! :)

  1. 👍 0
  2. 👎 0
  3. 👁 307
asked by Holly
  1. a) take the inverse of your function and show that the original equation comes back at you.

    b) for VA, the denominator is zero, so x-k = 0 is the vertical asymptote
    for a HA, I visualize what happens to kx/(x-k) as x -- ∞

    I see y = k

    c) I solved y = kx/(x-k) with y = x+2k and got
    x = ± k√2

    put each of those values back into your straight line equation to get the corresponding y's.

    take the derivative of the first function using the quotient rule, sub in the points you found to get the slope.

    Now that you have the slope and the point, find the straight line equation of the tangent.

    (I am assuming you know how to follow those steps)

    1. 👍 0
    2. 👎 0
    posted by Reiny
  2. a)
    the reflection matrix about the line y=x is
    0 1
    1 0
    In other words, new x = old y
    and new y = old x
    So what happens if we do this operation on and x old = a and a y old = b? (a,b)
    the original would be:
    b = (ka)/(a - k)
    find new x and new y if the symmetry exists (b,a)
    a = (kb)/(b-k)
    If that is true, we have the symmetry.
    so solve for b
    b a - k a = k b
    b (a-k) = k a
    b = (ka)/(a-k)

    1. 👍 0
    2. 👎 0
    posted by Damon

Respond to this Question

First Name

Your Response

Similar Questions

  1. trigonometry help please :(

    2) Simplify √-1-4/5-√-1 A.-1/24+19/24i B.-21/26+1/26i C.-19/24-1/24i D.-1/26-21/26i 3) How many petals do the two rose curves r = 9 cos 61θ and r = 8 sin 60θ have combined? A. 182 B. 242 C. 181 D. 131 4)What is true of the

    asked by suzy on August 16, 2013
  2. math

    Determine whether the function is symmetric with respect to the y-axis, symmetric with respect to the x-axis, symmetric with respect to the origin, or none of these. y = -6x3 + 7x

    asked by jeff on January 12, 2017
  3. Pre-Calculus-check answers

    The graph of the equation y=x^3-x is symmetric with respect to which of the following? a) the x-axis b) the y-axis c) the origin d) none of these Answer: c 2) The graph of an odd function is symmetric with respect to which of the

    asked by Lucy on August 10, 2008
  4. Trigonometry

    1. Which of the following statements are true? (i) r = 4 – 3 sin θ is the equation for a limaçon rotated 90°. (ii) r = 3 cos 8θ is the equation for a rose curve with 8 petals. (iii) rθ = 16 is the equation for a circle. A.

    asked by Suzy on August 16, 2013
  5. Trigonometry

    1. Which of the following statements are true? (i) r = 4 – 3 sin θ is the equation for a limaçon rotated 90°. (ii) r = 3 cos 8θ is the equation for a rose curve with 8 petals. (iii) rθ = 16 is the equation for a circle. A.

    asked by Suzy on August 16, 2013
  6. Math Analysis

    Tell if the function is symmetric with respect to the x-axis, y-axis, and origin. 3. 8x^2 - 2y^2 = 12 ==> I got that it was symmetric to both the x- and y-axes. Is this right? 4. 5x^2 - 3y^2 = 18 ==> I can't get anywhere with this

    asked by Emily on October 19, 2009
  7. Math

    Is the following function symmetric with respect to the y-axis, symmetric with respect to the x-axis, symmetric with respect to the origin, or none of the above? f(x)=-5x^3+2x I think it is: -3+1=2 This function is symmetric to

    asked by Tim on March 28, 2008
  8. Pre-Calc

    Could somebody please check this for me? Dtermine whether the graph of each equation is symmetric with respect to the origin, the x-axis, the y-axis, and the line y=x or the line y=-x. I came up with the line being symmetric to

    asked by Natalie on October 8, 2007
  9. Pre-calculus

    1. The graph of the equation y = x2 – 3 is symmetric with respect to which of the following? The answer is the y-axis . why? 2.The graph of an odd function is symmetric with respect to which of the following? the origin is the

    asked by billy on April 6, 2012
  10. maths2

    Test the equation for symmetry with respect to the x-axis, the y-axis, and the origin. x2 + y2 + x2y2 = 4 A. Symmetric with respect to the x-axis B. Symmetric with respect to the y-axis C. Symmetric with respect to the origin D.

    asked by mdan on October 12, 2013

More Similar Questions