The asymptote(s) of the graph of \(y=\log _e(x+1)-3\) are
- \(x=-1\) only
- \(x=1\) only
- \(y=-3\) only
- \(x=-1\) and \(y=-3\)
Functions, 2ADV 2021 HSC 3 MC
Which of the following represents the domain of the function `f(x)=ln(1-x)`?
- `[1,oo)`
- `(1, oo)`
- `(–oo, 1]`
- `(–oo, 1)`
Functions, 2ADV F2 2019 HSC 1 MC
What is the domain of the function `f(x) = ln(4-x)`?
- `x < 4`
- `x <= 4`
- `x > 4`
- `x >= 4`
Functions, 2ADV F2 EQ-Bank 22
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`
Show Worked Solution
`text(Asymptote when)\ x = 3`
`text(Domain)\ {x: \ x > 3}`
`text(Range: all)\ y`
Functions, 2ADV F2 EQ-Bank 23
The diagram below shows part of the graph of the function with rule
`f (x) = k log_e (x + a) + c`, where `k`, `a` and `c` are real constants.
- The graph has a vertical asymptote with equation `x = -1`.
- The graph has a y-axis intercept at 1.
- The point `P` on the graph has coordinates `(p, 10)`, where `p` is another real constant.
- State the value of `a`. (1 mark)
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- Find the value of `c`. (1 mark)
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- Show that `k = 9/(log_e (p + 1)`. (2 marks)
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Functions, 2ADV F2 EQ-Bank 12
- Draw the graph `y = ln x`. (1 mark)
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- Explain how the above graph can be transformed to produce the graph
- `y = 3ln(x + 2)`
- and sketch the graph, clearly identifying all intercepts. (3 marks)
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a.
b.
Show Worked Solution
a.
b. `text(Transforming)\ \ y = ln x => \ y = ln(x + 2)`
`y = ln x\ \ =>\ text(shift 2 units to left.)`
`text(Transforming)\ \ y = ln(x + 2)\ \ text(to)\ \ y = 3ln(x + 2)`
`=>\ text(increase each)\ y\ text(value by a factor of 3)`