The graph of \(y=f(x)\), where \(f(x)=a|x-b|+c\), passes through the points \((3,-5), (6,7)\) and \((9,-5)\) as shown in the diagram. --- 6 WORK AREA LINES (style=lined) --- --- 5 WORK AREA LINES (style=lined) ---
Functions, 2ADV F2 2022 HSC 19
The graph of the function `f(x)=x^2` is translated `m` units to the right, dilated vertically by a scale factor of `k` and then translated 5 units down. The equation of the transformed function is `g(x)=3 x^2-12 x+7`.
Find the values of `m` and `k`. (3 marks)
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Functions, 2ADV F2 SM-Bank 16
Let `f(x) = x^2 - 4`
Let the graph of `g(x)` be a transformation of the graph of `f(x)` where the transformations have been applied in the following order:
• dilation by a factor of `1/2` from the vertical axis (parallel to the horizontal axis)
• translation by two units to the right (in the direction of the positive horizontal axis
Find `g(x)` and the coordinates of the horizontal axis intercepts of the graph of `g(x)`. (3 marks)
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Functions, 2ADV F2 EQ-Bank 13
The curve `y = kx^2 + c` is subject to the following transformations
-
- Translated 2 units in the positive `x`-direction
- Dilated in the positive `y`-direction by a factor of 4
- Reflected in the `y`-axis
The final equation of the curve is `y = 8x^2 + 32x - 8`.
- Find the equation of the graph after the dilation. (1 mark)
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- Find the values of `k` and `c`. (2 marks)
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Functions, 2ADV F2 EQ-Bank 14
List a set of transformations that, when applied in order, would transform `y = x^2` to the graph with equation `y = 1 - 6x - x^2`. (3 marks)
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Functions, 2ADV F2 EQ-Bank 2 MC
Which diagram best shows the graph
`y = 1 - 2(x + 1)^2`
A. | B. | ||
C. | D. |
Functions, 2ADV F2 EQ-Bank 16
`y = -(x + 2)^4/3` has been produced by three successive transformations: a translation, a dilation and then a reflection.
- Describe each transformation and state the equation of the graph after each transformation. (2 marks)
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- Sketch the graph. (1 mark)
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Functions, 2ADV F2 EQ-Bank 1
Functions, 2ADV F2 SM-Bank 7 MC
The point `A (3, 2)` lies on the graph of the function `f(x)`. A transformation maps the graph of `f(x)` to the graph of `g(x)`,
where `g(x) = 1/2 f(x - 1)`. The same transformation maps the point `A` to the point `P`.
The coordinates of the point `P` are
A. `(2, 1)`
B. `(2, 4)`
C. `(4, 1)`
D. `(4, 2)`
Functions, 2ADV F2 SM-Bank 6 MC
The graph of a function `f(x)` is obtained from the graph of the function `g(x) = sqrt (2x - 5)` by a reflection in the `x`-axis followed by a dilation from the `y`-axis by a factor of `1/2`.
Which one of the following is the function `f(x)`?
A. `f(x) = sqrt (5 - 4x)`
B. `f(x) = - sqrt (x - 5)`
C. `f(x) = sqrt (x + 5)`
D. `f(x) = −sqrt (4x - 5)`
Functions, 2ADV F2 SM-Bank 5 MC
The point `P\ text{(4, −3)}` lies on the graph of a function `f(x)`. The graph of `f(x)` is translated four units vertically up and then reflected in the `y`-axis.
The coordinates of the final image of `P` are
- `(-4, 1)`
- `(-4, 3)`
- `(0, -3)`
- `(4, -6)`
Functions, 2ADV F2 SM-Bank 4 MC
The graph of the function `f(x) = 3x^(5/2)` is reflected in the `x`-axis and then translated 3 units to the right and 4 units down.
The equation of the new graph is
A. `y = 3(x - 3)^(5/2) + 4`
B. `y = -3 (x - 3)^(5/2) - 4`
C. `y = -3 (x + 3)^(5/2) - 1`
D. `y = -3 (x - 4)^(5/2) + 3`
Functions, 2ADV F2 SM-Bank 1
- 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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Functions, 2ADV F2 2013 HSC 15c
- Sketch the graph `y = |\ 2x - 3\ |`. (1 mark)
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- Using the graph from part (i), or otherwise, find all values of `m` for which the equation `|\ 2x - 3\ | = mx + 1` has exactly one solution. (2 marks)
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