Question

Let (-4, -2) be a point on the graph of y=f(x). Under the transformation y=3f(x) + 2. The point (-4, -2) will be translated to what point?

a .(-4, -4)
b .(-12, -4)
c. (-12, 0)
d .(-4, 0)

Answer 1

The original point (-4, -2) undergoes the transformation y=3f(x)+2. Just the y-value is affected, tripling and then increasing by 2, to get the new point (-4, -4).

Step-by-step explanation:

The student's question involves a point transformation under a function. Let's start with the original point given, which is (-4, -2). The point is on the graph of the function y = f(x). The transformation applied to the function is y = 3f(x) + 2. To find the new coordinates of the point after the transformation, we multiply the y-value of the point by 3 and then add 2 (since that's what the transformation tells us to do to f(x)). As the x-value remains unchanged, we only need to apply this to the y-value.

f(x) at x = -4 is -2, therefore applying the transformation 3(-2) + 2 we get 3(-2) + 2 = -6 + 2 = -4.

Thus, the new y-value for the point after the transformation is -4 and the x-value remains -4.

Therefore, the transformed point is (-4, -4).