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Functions and Graphs : Sketching, Domain, Range and Asymptotes

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1. The length of a rectangular field is 3 times its width. If fencing costs $12 per metre, express the cost, C, of fencing the field as a function of the width, w.
2. Draw a set of axes and then plot the graph of the function f(x) = 2x ?4, for
3. (i) On a set of axes, sketch the graph of f(x) = x2 + 4x ? 1 for ?6 x 2.
Clearly show the points where the function crosses each axis and the point
where the function has its minimum value.
(ii) Describe, in words, how the graph of f(x) = (x + 1)2 + 4(x + 1) ? 1
would look on the same set of axes.
Sketch the function g(x) = , clearly showing the two asymptotes for the x+2
Given that f(x) = + 3x ? x2, write down:
(i) f(-3)
(i) f(h)
(iii) f(3+h),
(iv) f(3+h)/h

6. Draw a set of axes, show the region for which 0 x 1 and 0 y 5.
Find the domain and range of the function f(x) = ? x. On a set of axes, give a sketch graph of f(x).