Algebraic to algebraic transformation description

2

1. The graph of \(y = \mathrm { f } ( x )\) is transformed to the graph of \(y = 2 \mathrm { f } ( x - 1 )\).
   Describe fully the two single transformations which have been combined to give the resulting transformation.
2. The curve \(y = \sin 2 x - 5 x\) is reflected in the \(y\)-axis and then stretched by scale factor \(\frac { 1 } { 3 }\) in the \(x\)-direction. Write down the equation of the transformed curve.

2 The curve \(y = x ^ { 2 }\) is transformed to the curve \(y = 4 ( x - 3 ) ^ { 2 } - 8\).
Describe fully a sequence of transformations that have been combined, making clear the order in which the transformations have been applied.

2 The graph of \(y = \mathrm { f } ( x )\) is transformed to the graph of \(y = 1 + \mathrm { f } \left( \frac { 1 } { 2 } x \right)\).
Describe fully the two single transformations which have been combined to give the resulting transformation.

1 The graph of \(y = \mathrm { f } ( x )\) is transformed to the graph of \(y = 3 - \mathrm { f } ( x )\).
Describe fully, in the correct order, the two transformations that have been combined.

5

1. Th cn \(y = x ^ { 2 } + 3 x + 4\) s tras latedy \(\binom { 2 } { 0 }\).
   Find imp ify \(\mathbf { b }\) eq tim the tras lated \(\mathrm { n } \mathbb { E }\).
2. Th g ad \(y = \mathrm { f } ( x )\) is tras fo med \& b g ap \(6 y = \mathrm { B } ( - x )\). Describ fly ly th two sig le tras fo matin wh ch hav b en cm be d to ge th resh tig tras fo matio
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9

1. Describe fully a sequence of transformations that map the line \(y = x\) onto the line $$y = 10 - 2 x$$ The function f is defined as \(\mathrm { f } : x \rightarrow 10 - 2 x , x \in R , x \geq 0\).
   The function ff is denoted by g .
2. Find \(\mathrm { g } ( x )\), giving your answer in a form without brackets.
3. Determine the domain of g .
4. Explain whether \(\mathrm { fg } = \mathrm { gf }\).
5. Find \(\mathrm { g } ^ { - 1 }\) in the form \(\mathrm { g } ^ { - 1 } : x \rightarrow \ldots\)