Question

The function represents f(x) = 9cos(x - π/2) + 3, translating π/6 units left and 4 units up. Which equation represents g(x)?

A. g(x) = 9cos(x - π/3) - 1
B. g(x) = 9cos(x - π/3) + 7
C. g(x) = 9cos(x - (2π)/3) - 1
D. g(x) = 9cos(x - (2π)/3) + 7

Answer 1

The correct answer is option B, which is g(x) = 9cos(x - π/3) + 7, representing a translation of the original cosine function to the left and upwards.

Step-by-step explanation:

The question involves finding the equation for the function g(x) which represents a transformed version of another trigonometric function f(x). Initially, f(x) = 9cos(x - π/2) + 3, and the transformation involves translating the graph π/6 units to the left and 4 units up. To translate a function to the left, we adjust the inside of the cosine function by adding π/6 to the existing phase shift, resulting in a new phase shift of -π/2 + π/6 = - π/3. Adjusting the vertical shift entails simply adding 4 to the original vertical shift of 3, for a new vertical shift of 7. Therefore, the new function is g(x) = 9cos(x - π/3) + 7, making option B the correct answer.