Question

What are the values of a, b, h, and k, and how would you describe the transformations for the function f(x)=−2∣3(x−4)∣?

a) a=−2,b=3,h=4,k=0
b) a=−2,b=3,h=−4,k=0
c) a=2,b=−3,h=−4,k=0
d) a=2,b=3,h=4,k=0

Answer 1

The function f(x)=-2|3(x-4)| is stretched vertically by a factor of 2, reflected over the x-axis, stretched horizontally by a factor of 1/3, and shifted to the right by 4 units. The values for a, b, h, and k are -2, 3, 4, and 0, respectively.

Step-by-step explanation:

The function f(x)=−2|3(x−4)| can be described by determining the values of a, b, h, and k in the general form of a transformed absolute value function, which is f(x) = a|b(x - h)| + k. In this case, the values areThe values of a, b, h, and k for the function f(x) = -2|3(x - 4)| are:a = -2, b = 3, h = 4, k = 0The transformations for the function are a reflection in the x-axis (-2 factor multiplying the function),

a horizontal compression by a factor of 1/3 or a stretching by a factor of 3 in the x-direction (3 factor inside the absolute value), and a horizontal shift 4 units to the right (x - 4 inside the absolute value).