The figure shows the graphs of the functions y = f(x) and y = g(x). The four indicated points all have integer coefficients.

If g(x) = k∙f(x), what is the value of k?

This question is comparing the stretch of f(x) to arrive at g(x).

These two are combined, in this particular situation, to create a stretch and a reflection.

Note on f(x), the point (1,-1).

Also note on g(x), the point (1,3).

For an x value of 1, the y-value is multiplied by -3.

Note on f(x), the point (0,1).

Also note on g(x), the point (0,-3).

For an x value of 0, the y-value is multiplied by -3.

**A graph is stretched away from the x-axis by multiplying the y-value by a number greater than 1.****A graph is reflected over the x-axis by taking the negative of the y-value.**These two are combined, in this particular situation, to create a stretch and a reflection.

Note on f(x), the point (1,-1).

Also note on g(x), the point (1,3).

For an x value of 1, the y-value is multiplied by -3.

Note on f(x), the point (0,1).

Also note on g(x), the point (0,-3).

For an x value of 0, the y-value is multiplied by -3.

**Thus, since the y-value in f(x) is being multiplied by -3,**

a stretch of 3 and a reflection over the x-axis are created to arrive at g(x).a stretch of 3 and a reflection over the x-axis are created to arrive at g(x).

**k = -3**

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