The diagram shows the graph of the function \(y=f(x)\). On the diagram, sketch the graph of \(y=\dfrac{1}{f(x)}\), stating the range in set notation. (3 marks) --- 4 WORK AREA LINES (style=lined) --- \(\text{Range}\ y=\dfrac{1}{f(x)}: \Big(-\infty, -\dfrac{1}{2}\Big)\ \cup\ \Big[\dfrac{2}{3}, \infty\Big)\) \(\text{Range}\ y=\dfrac{1}{f(x)}: \Big(-\infty, -\dfrac{1}{2}\Big)\ \cup\ \Big[\dfrac{2}{3}, \infty\Big)\)
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Functions, EXT1 F1 2020 HSC 11c
The diagram shows the graph of `y = f(x)`.
Sketch the graph of `y = 1/(f(x))`. (3 marks)
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Functions, EXT1′ F1 2008 HSC 3a
The following diagram shows the graph of `y = g(x)`.
Draw separate one-third page sketches of the graphs of the following:
- `y = |g(x)|` (1 mark)
--- 8 WORK AREA LINES (style=lined) ---
- `y = 1/(g(x))` (2 marks)
--- 8 WORK AREA LINES (style=lined) ---
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Functions, EXT1 F1 SM-Bank 12
Given `f(x) = x^3 - x^2 - 2x`, without calculus sketch a separate half page graph of the following functions, showing all asymptotes and intercepts.
- `y = |\ f(x)\ |` (1 mark)
--- 8 WORK AREA LINES (style=lined) ---
- `y = f(|x|)` (2 marks)
--- 8 WORK AREA LINES (style=lined) ---
- `y = 1/(f(x))` (2 marks)
--- 10 WORK AREA LINES (style=lined) ---
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| i. | `f(x)` | `= x^3 – x^2 – 2x` |
| `= x(x^2 – x – 2)` | ||
| `= x(x – 2)(x + 1)` |
ii.
`y = f(|x|)\ text(is a reflection of)\ y = f(x)\ text(for)\ x > 0`
`text(is the)\ ytext(-axis.)`
iii.
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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Functions, EXT1′ F1 2009 HSC 3a
The diagram shows the graph `y = f(x).`
Draw separate one-third page sketches of the graphs of the following:
- `y = 1/(f(x)) .` (2 marks)
--- 8 WORK AREA LINES (style=lined) ---
- `y = f(x)\ f(x)` (2 marks)
--- 12 WORK AREA LINES (style=lined) ---
- `y = f(x^2).` (2 marks)
--- 8 WORK AREA LINES (style=lined) ---
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i. `text(Vertical asymptotes at)\ \ x=0 and 4`
`text(Horizontal asymptote at)\ \ y=-1/3`
ii. `y=f(x)\ f(x) = [f(x)]^2`
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iii. `y=f(x^2) =>text(even function)`
`text(When)\ \ x=±2,\ \ y=f(4)=0`
Functions, EXT1′ F1 2010 HSC 3a
- Sketch the graph `y = x^2 + 4x`. (1 mark)
--- 8 WORK AREA LINES (style=lined) ---
- Sketch the graph `y = 1/(x^2 + 4x)`. (2 marks)
--- 10 WORK AREA LINES (style=lined) ---
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Functions, EXT1′ F1 2014 HSC 12a
The diagram shows the graph of a function `f(x)`.
Draw a separate half-page graph for each of the following, showing all asymptotes and intercepts.
- `y = f(|\ x\ |)` (2 marks)
--- 10 WORK AREA LINES (style=lined) ---
- `y = 1/(f(x))` (2 marks)
--- 10 WORK AREA LINES (style=lined) ---
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