If f(X) has the point (-3, -27), find the y-value given g(x)=-1/3 f (x+2)-5 and find the point on the transformed function

Answer 1

HI Shiloh,

Refer to y=Af[B(x-C)]+D, where A is the vertical stretch or shrink factor, B is the horizontal stretch or shrink factor, C is the horizontal translation, and D is the horizontal translation.

The "-1/3" is going to affect the y-coordinate by reflecting it over the x-axis (because of the negative) and shrinking it (vertically) by a factor of 1/3: -27*-1/3=9. (Note had B been -1/3, the x coordinate would be multiplied by the reciprocal, -3).

The "+2" is going to affect the x-coordinate by shifting it left (not right) by two units: -3-2=-5

The "-5" affects the new y-coordinate by translating it down (not up) by 5 units: 9-5=4

So, (-5,4).