Algebra

Function Graphs

Stretching Graphs

         

Given the graph y=4x2+9 y = 4x^2+9 , how do we obtain the graph of y=196x2+9? 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(x4)2+8y=9(x-4)^2+8 by a factor of  5\ 5 in the yy-direction?

Note: The above graph is not drawn to scale.

What is the equation of the resulting graph after stretching y=7sin(8πx)y=7\sin(8\pi x) by a factor of 18\frac{1}{8} with respect to the xx-axis?

Note: The above graph is not drawn to scale.

If the graph of 49x2+9y2=2549x^2+9y^2=25 undergoes stretching by a factor of a>0a > 0 with respect to the xx-axis and stretching by a factor of b>0b >0 with respect to the yy-axis such that the resulting graph is a circle of radius 55, what are aa and b?b?

What is the equation of the resulting graph after stretching y=8x2+9x+6y=-8x^2+9x+6 by a factor of 16\frac{1}{6} horizontally and by a factor of 22 vertically?

Note: The above graph is not drawn to scale.

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