Math CentralQuandaries & Queries


Question from Kevin, a student:

Could you please show me what change y=f(x) to y=-3/2f(x) has gone through and please graph.

y=f(x) points: (-3,0) ,(0,-2), (2,-2), (3,4)

how does (0,-2) change?

Hi Kevin,

I am going to change the name of the second expression so it is clear which one I am referring to. The first expression is $y = f(x)$ and the second is $z = \frac{-3}{2} f(x).$

The second expression multiplies each value of the first expression by the fraction $\frac{-3}{2}.$ Thus if $(3,4)$ is a point that satisfies the first expression $y = f(x)$ (that is $f(3) = 4)$ then the corresponding point that satisfies $z = \frac{-3}{2} f(x)$ is $(3, \frac{-3}{2} \times 4) = (3, -6).$

Thus, if you have a point on the graph of the $y$ expression then the corresponding point on the graph of the $z$ expression has the same first coordinate but the second coordinate is $\frac{-3}{2}$ times the second coordinate of the point on the graph of the $y$ expression.

I hope this helps,

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