Flashcards · Maths · Functions, Sequences and Rates of Change
Transformations of Graphs
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What does \(y = f(x) + a\) do to the graph?
Translates it up by \(a\).
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What does \(y = f(x + a)\) do to the graph?
Translates it left by \(a\).
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What does \(y = f(x - a)\) do to the graph?
Translates it right by \(a\).
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What does \(y = -f(x)\) do to the graph?
Reflects it in the \(x\)-axis.
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What does \(y = f(-x)\) do to the graph?
Reflects it in the \(y\)-axis.
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Where does \((3, 5)\) move to under \(y = f(x) - 4\)?
\((3, 1)\).
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Where does \((3, 5)\) move to under \(y = f(x - 2)\)?
\((5, 5)\).
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Where does \((3, 5)\) move to under \(y = f(-x)\)?
\((-3, 5)\).
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Where does \((3, 5)\) move to under \(y = -f(x)\)?
\((3, -5)\).
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What is the equation of \(y = x^2\) moved 3 units right?
\(y = (x - 3)^2\).
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What is the equation of \(y = x^2\) moved 2 units up?
\(y = x^2 + 2\).
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What is \(\sin(x + 90^\circ)\) equal to?
\(\cos x\).
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What is the maximum of \(y = \sin x + 1\)?
2.
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Which way does a minus outside the bracket reflect?
In the \(x\)-axis.
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How do you sketch a transformation?
Follow a key point, such as a turning point, and redraw.
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Which tier are graph transformations?
Higher tier on all boards.