-3
29. [Maximum mark: 24] [without GDC)
The function f is given by f(x) = 2x+1, xeR, X+3.
(a) (0) Show that y=2 is an asymptote of the graph of y=f(x).
(ii) Find the vertical asymptote of the graph.
(ii) Write down the coordinates of the point P at which the asymptotes intersect.
(b) Find the points of intersection of the graph and the axes.
(c) Hence sketch the graph of y = f(x), showing the asymptotes by dotted lines.
(d) Show that f'(x) =
-7
and hence find the equation of the tangent at
(x-3)
the point S where r=4.
[4]
[4]
[4]
[6]
(e) The tangent at the point T on the graph is parallel to the tangent at S.
Find the coordinates of T.
(6)
Show that P is the midpoint of (ST).
1
]
[5]
[1]
MacD
