1. By drawing up a short table of values, sketch the graphs of the following cubic functions:...

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1. By drawing up a short table of values, sketch the graphs of the following cubic functions:

(a) y = x 2x - 7x-4 (b) y = 4x8x-3x+5


2. The cubic function f(x) is defined by

f(x) = 54x-270x +450x-266

(a) Sketch the graph of f (x) for x = 0, 1, 2 and 3 only, hence estimate the value of a zero of f (x) .

(b) Observing that f(x) = 0 implies that (3x − 5)3 = 8 find the exact value of this root.


3. By tabulating values for x from −3 to 3 in steps of 1 draw a graph of the cubic function y = f(x) = 2x3 + x2 − 5x + 2

(a) Locate (approximately) the roots of the function from your graph.

(b) Confirm your answers to (a) by determining the values of f(−2), f (1) and f(1/2)


4. An ashtray is made by taking the square of metal ABCD of side 12 cm (see Figure 8.7)
and removing the four squares of side x cm from each of the corners. Folding along the
lines EF, FG, GH, HE then forms an ashtray of depth x cm

12cm A D r E F 12cm H G--- Gr X B  Figure 8.7 Design of ashtray X

Prove that the volume V of the ashtray is given by

V =4x(6-x)

Draw the graph of V against x for values of x between 0 and 7. From your graph

(1) (11) state the maximum possible volume for the ashtray and the fraction of metal removed in making the

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