The function `f(x) = x^3` is transformed to `g(x) = (x - 2)^3 + 5` by a horizontal translation of 2 units followed by a vertical translation of 5 units.
Which row of the table shows the directions of the translations?
Functions, 2ADV F1 SM-Bank 35
- Sketch the function `y = f(x)` where `f(x) = (x - 1)^3` on a number plane, labelling all intercepts. (1 mark)
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- On the same graph, sketch `y = −f(−x)`. Label all intercepts. (2 marks)
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i. `y = (x – 1)^3 => y = x^3\ text(shifted 1 unit to the right.)`
ii. `y = −f(x) \ => \ text(reflect)\ \ y = (x – 1)^3\ \ text(in)\ xtext(-axis).`
`y = −f(−x) \ => \ text(reflect)\ \ y = −f(x)\ \ text(in)\ ytext(-axis).`
Functions, 2ADV F2 SM-Bank 2
Sketch the graph `y = log_2(x - 3)`.
Show all asymptotes and state its domain and range. (3 marks)
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`text(Domain)\ {x: \ x > 3}`
`text(Range: all)\ y`
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`text(Asymptote when)\ x = 3`
`text(Domain)\ {x: \ x > 3}`
`text(Range: all)\ y`
Functions, 2ADV F2 2016 HSC 3 MC
Which diagram best shows the graph of the parabola `y = 3 - (x - 2)^2?`
Functions, 2ADV F2 2006 HSC 1c
Sketch the graph of `y = |\ x + 4\ |`. (2 marks)
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Functions, 2ADV F2 2014 HSC 2 MC
Which graph best represents `y = (x - 1)^2`?
