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Function Graphs

Graphs are visual representations of functions. If you know how to read graphs, you can say a lot about a function just by looking at its graph. Learn this fine art of mathematical divining.

Translating Graphs

         

The above graph is the result of parallel translation of \(y = x^2.\) If this graph undergoes an additional translation of \(5\) in the positive direction of the \(x\)-axis and an additional translation of \(6\) in the positive direction of the \(y\)-axis, what is the equation of the resulting graph?

If the graph of the above circle with center \((3,5)\) and radius \(4\) undergoes a translation of \(4\) in the positive direction of the \(x\)-axis and \(5\) in the positive direction of the \(y\) axis, what is the equation of the resulting graph in quadratic form?

If the graph of \( y = -8 x^2 -80 x -38\) undergoes a translation of \(-3\) in the positive direction of the \(x\)-axis and \(3\) in the positive direction of the \(y\)-axis, what is the equation of the resulting graph?

If the above graph of \( y = 9 x^3\) is the result of a parallel translation of the equation \(y=f(x)\) by \(- 5\) in the positive direction of the \(x\)-axis followed by a translation of \(- 3\) in the positive direction of the \(y\)-axis, what is the equation \(y=f(x)?\)

If the graph of \( y = 5 (x-5)^2 + 7\) undergoes a translation of \(3\) in the positive direction of the \(x\) axis and \(-1\) in the positive direction of the \(y\)-axis, what is the equation of the resulting graph?

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