--- 5 WORK AREA LINES (style=lined) --- --- 8 WORK AREA LINES (style=lined) --- \(\text{Domain:}\ \ 3 x-1 \ \geqslant 0 \ \Rightarrow \ x \geqslant \dfrac{1}{3}\) \(\text {Range:}\ \ y \geqslant 0\) ii. \(\text{Domain:}\ \ 3 x-1 \ \geqslant 0 \ \Rightarrow \ x \geqslant \dfrac{1}{3}\) \(\text {Range:}\ \ y \geqslant 0\) ii.
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i.
\(f(x)\)
\(=3x-1\)
\(y\)
\(=\sqrt{3x-1}\)
Show Worked Solution
i.
\(f(x)\)
\(=3x-1\)
\(y\)
\(=\sqrt{3x-1}\)
Functions, EXT1′ F1 2019 HSC 6 MC
Which graph best represents `y^2 = 2sin |\ x\ |`?
| A. |  |
B. |  |
| C. |  |
D. |  |
Functions, EXT1 F1 EQ-Bank 13
The diagram shows the graph of the function `g(x).`
Draw a half page graph of `y = sqrt(g(x)),` showing any asymptotes and stating its domain and range. (2 marks)
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Show Worked Solution
`text(Domain:)\ {x <= −2 \ ∪\ x >= 1}`
`text(Range:)\ {y >= 0}`
Functions, EXT1′ F1 2016 HSC 11d
The diagram shows the graph of `y = f(x).`
Draw a separate half-page diagram for each of the following functions, showing all asymptotes and intercepts.
- `y = sqrt (f(x))` (2 marks)
--- 8 WORK AREA LINES (style=lined) ---
- `y = 1/(f(x))` (2 marks)
--- 8 WORK AREA LINES (style=lined) ---
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| i. |
|
| ii. |
|
Show Worked Solution
| i. |  |
| ii. |  |
Functions, EXT1′ F1 2016 HSC 1 MC
Which equation best represents the following graph?
- `y = sqrt x`
- `|\ y\ | = sqrt x`
- `y = sqrt (|\ x\ |)`
- `|\ y\ |\ = sqrt (|\ x\ |)`
Functions, EXT1′ F1 2014 HSC 5 MC
Which graph best represents the curve `y^2 = x^2 - 2x`?
Show Worked Solution
| `text(S)text(ince)\ \ y^2` | `>0` |
| `x^2 – 2x` | `>0\ \ \ text(which is undefined for)\ \ 0 < x < 2` |
`=>C`
`text(Alternative Solution)`
`text(Consider)\ \ y = x^2 − 2x\ \ text{(above)}`
| `y` | `= ±sqrt(x^2 − 2x)` |
`text(This curve is undefined for)\ \ 0 < x < 2.`
`=> C`
Functions, EXT1′ F1 2013 HSC 13b
The diagram shows the graph of a function `f(x).`
Sketch the following curves on separate half-page diagrams.
- `y^2 = f(x).` (2 marks)
--- 8 WORK AREA LINES (style=lined) ---
- `y = 1/(1 - f(x)).` (3 marks)
--- 12 WORK AREA LINES (style=lined) ---
Show Worked Solution
i. `y^2 = f(x)`
`text(Only exist for)\ \ f(x) >= 0`
`y^2 = 1,\ \ \ y = +- 1`
ii. `y = 1/(1 – f(x))`
MARKER’S COMMENT: Correct working sketches such as `y=-f(x)` and `y=1-f(x)` meant that students could obtain some marks, even if their final sketch was wrong. Note this important advice.
`f(x) = 1,\ \ \ y\ text(undefined.)`
`f(x) > 1,\ \ \ y < 0`
`f(x) <= 0, \ \ \ y <= 1`
