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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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