# Calc problem

posted by .

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.

• Calc problem -

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)

• Calc problem -

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)

## Similar Questions

1. ### Vectors

I am really lost and confused! Consider the lines r = (1,-1,1) + t(3,2,1) and r = (-2,-3,0) + u(1,2,3). a) Find their point of intersection. b) Find a vector equation for the line perpendicular to both of the given lines that passes …
2. ### Functions

(a)Consider the function: f(x)=(7x+13)/(13x-1) (i)Calculate the exact values of the coordinates of the points of intersection of the graph of this function with the coordinate axes. (ii)Calculate the equations of the asymptotes (b)The …
3. ### Functions

(a)Consider the function: f(x)=(7x+13)/(13x-1) (i)Calculate the exact values of the coordinates of the points of intersection of the graph of this function with the coordinate axes. (ii)Calculate the equations of the asymptotes (b)The …
4. ### calculus

final question Consider the function F(x)=3x^4-5x+3 / X^4+1 Find: Domain Vertical,horizontal,or slant asymptotes x-intercept(s) y-itercept(s) symmetry(respect to x, y-axis or orgin) F’ (x) Critical numbers F” (x) Possible points …
5. ### Math

Find parametric equations and symmetric equations for the line of intersection of the given planes. x + y + z = 2, x + z = 0 X=1 y = Z= x=, y=

7. ### Algebra 2

Identify all horizontal and vertical asymptotes of the graph of the function. f(x)=x^2/x^2-4 I know the vertical asymptotes are x=2 and x=-2, but how do I find the horizontal asymptotes?
8. ### Math Functions

f(x)= 3x+2/2x+4 graph the function horizontal and vertical asymptotes. Show the table. I found the horizontal and vertical asymptotes, but im confused on how to do a table
9. ### Pre-Calc

Find the vertical asymptotes, if any, of the graph of the rational function. Show your work. f(x) = (x-4)/(x(x-4)) How would I show my work?
10. ### PRE-CALC

I am given the rational function: f(x)= (x^3 - 1) / (x^2 - 4) I found that the domain is all real numbers except x= plus or minus 2 , I also found that the x intercept is x=1, however I do not get how to find: the y-intercet , or identify …

More Similar Questions