Tangent to a Curve (Edexcel)

Hii,
I'm doing a Math paper, and I'm stuck on one part of a question..(I know I'm gonna be stuck on the last three too!) :-

QUESTION
a) Describe fully a single transformation that maps the graph of y = 1/x onto the graph of y = 3/x.
b) Sketch the graph of y = 3/x and write down the equations of any asymptotes.
c) Find the values of the constant c for which the straight line y = c - 3x is a tangent to the curve y = 3/x.

This is what I've done so far...:-

ANSWERS
a) vertical stretch in the y-direction, multiple factor = 3.
b) (I've sketched the graph and plotted some points) When x = 0, y is not defined (vertical asymptote). When y = 0, x is not defined (horizontal asymptote). Therefore, as x tends towards +ve and -ve infinity, y tends to zero and as y tends towards =ve and -ve infinity, x tends to zero.
c) :s HELPPP!!

I have no idea what to do for part c, I've made the line equal but it doesn't make any sense. Any help would be appreciated, THANKS! :smile:

Reply 1

neomilan

c) If you think about the shape of the graph it is clear that the straight line will only touch the curve once, so do quadratic formed by eliminating one of the variables such as y when finding the point of intersection wil have repeated root (b^2=4ac), use this fact to obtain a quadratic in c and hence find the value of c.

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