Question

The graph of the function f(x)=log6(x) is stretched vertically by a factor of 7, reflected over the x-axis, reflected over the y-axis, and shifted up by 2 units.

Answer 1

The resulting function after all transformations have been carried out is; -7log6(-x) - 2.

Which function results from all the Transformations?

The transformations which ensued on the function given are as follows;

• Stretched vertically by a factor of 7; Hence, we have; 7f(x) = 7log6(x).
• Reflected over the x-axis; -7f(x) = -7log6(x).
• Reflected over the y-axis; -7f(x) = -7log6(-x).
• Shifted up by 2 units; -7f(x) -2 = -7log6(-x) - 2.

On this note, it follows that the resulting function upon all the Transformations is; = -7log6(-x) - 2.

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