   SEARCH HOME Math Central Quandaries & 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,
Penny      Math Central is supported by the University of Regina and the Imperial Oil Foundation.