smc-1008-65-Dilation (Only)

Functions, 2ADV F2 2021 HSC 21

Consider the graph of `y = f(x)` as shown.

Sketch the graph of `y = 4f(2x)` showing the `x`-intercepts and the coordinates of the turning points. (2 marks)

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♦ Mean mark 48%.

Functions, 2ADV F2 SM-Bank 8 MC

The transformation that maps the graph of `y = sqrt(8x^3 + 1)` onto the graph of `y = sqrt(x^3 + 1)` is a

dilation by a factor of `2` from the `y`-axis.
dilation by a factor of `2` from the `x`-axis.
dilation by a factor of `1/2` from the `x`-axis.
dilation by a factor of `1/2` from the `y`-axis.

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`A`

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`text(Let)\ f(x)`	`= sqrt(8x^3 + 1)`
`f(1/2 x)`	`= sqrt(8(1/2 x)^3 + 1)`
	`= sqrt(x^3 + 1)`

`:.\ text(Transformation correct when)\ \ x\ \ text(is swapped for)\ \ x/2`

`text(i.e. graph is dilated by factor of 2 from)\ ytext(-axis)`

`=> A`