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The graph of y = 1/x is vertically stretched by a factor of 3, reflected across the y-axis and shifted to the left by 2 units. What it the function of the resulting graph?

y = 3/(x-2)
y = (-3)/(x+2)
y = 1/(3x-6)
y = (-1)/(3x+6)
y = (-1)/(3x-6)

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ANSWER

[tex]y = - \frac{3}{x + 2} [/tex]

EXPLANATION

The given parent function is:

[tex]y = \frac{1}{x} [/tex]

When this function is vertically stretched by a factor of 3, then we have

[tex]y = \frac{3}{x} [/tex]

A reflection across the y-axis transforms the function to;

[tex]y = - \frac{3}{x} [/tex]

When the resulting function is shifted to the left, the transformed function becomes;

[tex]y = - \frac{3}{x + 2} [/tex]