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).
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).
k = -3
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