Connect a factorised higher-degree rule and its graph practice questions | Mathematical Methods (Year 12, VCE Units 3 & 4, Functions and graphs, Linear and polynomial graphs)

Question 1 of 8

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The following exact rule defines P. Let \(P(x)\) be given by:

P(x)=2(x+2)(x+\frac{1}{3})(x-1)^{2}

An exact calibration point is \(P(-1)=-\frac{16}{3}\). Use the graph window \(-3\le x\le 3\) and \(-136\le y\le 336\) for the graph selection

(a)7 marks

Use the stated factorised rule to complete the table of ordered x-intercepts, their multiplicities and the vertical intercept

\(x\)-intercept 1 in increasing order multiplicity at \(x\)-intercept 1 \(x\)-intercept 2 in increasing order multiplicity at \(x\)-intercept 2 \(x\)-intercept 3 in increasing order multiplicity at \(x\)-intercept 3 vertical intercept \(P(0)\)

(b)1 mark

How does the graph meet the horizontal axis?

At x=-2, the graph crosses the horizontal axis without flattening. At x=-1/3, the graph crosses the horizontal axis without flattening. At x=1, the graph touches the horizontal axis and turns

The parity rule is reversed. At x=-2, the graph touches the horizontal axis and turns. At x=-1/3, the graph touches the horizontal axis and turns. At x=1, the graph crosses the horizontal axis

An odd repeated factor is treated as an ordinary crossing. At x=-2, the graph crosses the horizontal axis without flattening. At x=-1/3, the graph crosses the horizontal axis without flattening. At x=1, the graph touches the horizontal axis and turns

Repeated factors are treated as touch points. At x=-2, the graph crosses the horizontal axis. At x=-1/3, the graph crosses the horizontal axis. At x=1, the graph touches the horizontal axis and turns

What happens at the two outer ends of the graph?

The graph rises on both the left and the right

The graph falls on both the left and the right

The graph falls on the left and rises on the right

The graph rises on the left and falls on the right

(d)1 mark

Select the graph of P