iGCSE (2021 Edition)

By considering the graph of $y=x^3$`y`=`x`3, determine the following:

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a

As $x$`x` becomes larger in the positive direction (ie $x$`x` approaches infinity), what happens to the corresponding $y$`y`-values?

they approach zero

A

they become very large in the positive direction

B

they become very large in the negative direction

C

they approach zero

A

they become very large in the positive direction

B

they become very large in the negative direction

C

b

As $x$`x` becomes larger in the negative direction (ie $x$`x` approaches negative infinity), what happens to the corresponding $y$`y`-values?

they become very large in the positive direction

A

they approach zero

B

they become very large in the negative direction

C

they become very large in the positive direction

A

they approach zero

B

they become very large in the negative direction

C

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Sketch the graphs of cubic polynomials and their moduli, when given in factorised form y = k(x – a)(x – b)(x – c).