Solve the below:
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
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) =3/x+2 , clearly showing the two asymptotes for the x+2 function.
Given that f(x) = 12/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) = √5-x. On a set of axes, give a sketch graph of f(x).