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

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

(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

Prove that the volume V of the ashtray is given by

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

Transcribed Image Text:

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