Which curve best represents the graph of the function $f(x) = -a ext{sin} \, x + b ext{cos} \, x$ given that the constants a and b are both positive? - HSC - SSCE Mathematics Extension 1 - Question 7 - 2021 - Paper 1

1. The $-a \sin x$ component will create a wave that is inverted (flipped vertically), as it takes the sine function values and multiplies them by -a.

2. The $b \cos x$ component will contribute a cosine wave that oscillates above and below the x-axis with a maximum amplitude of +b.

By combining the inverted sine wave and the positive cosine wave, the resulting graph will be influenced more strongly by the cosine function (which yields positive peaks), while the sine contribution will lower the troughs.

Considering all the above observations, we can analyze the provided options (A, B, C, D). The correct graph that represents this function with the identified behaviors is option D.