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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.

Stretching Graphs

Given the graph \( y = 4x^2+9 \), how do we obtain the graph of \[ y = 196x^2 +9?\]

Note: The above graph is not drawn to scale.

What is the equation of the resulting graph after stretching \(y=9(x-4)^2+8\) by a factor of \(\ 5 \) in the \(y\)-direction?

Note: The above graph is not drawn to scale.

What is the equation of the resulting graph after stretching \(y=7\sin(8\pi x)\) by a factor of \(\frac{1}{8} \) with respect to the \(x\)-axis?

Note: The above graph is not drawn to scale.

If the graph of \(49x^2+9y^2=25\) undergoes stretching by a factor of \(a > 0\) with respect to the \(x\)-axis and stretching by a factor of \(b >0\) with respect to the \(y\)-axis such that the resulting graph is a circle of radius \(5\), what are \(a\) and \(b?\)

What is the equation of the resulting graph after stretching \(y=-8x^2+9x+6\) by a factor of \(\frac{1}{6} \) horizontally and by a factor of \(2\) vertically?

Note: The above graph is not drawn to scale.

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