Precalc question

Question

Determine the range of 𝑦 = −5cos(𝑥 + 𝜋) − 3

Answer 1

Normally, a cos curve will have a range of [-1,1] with a midline on the x axis. However there are 2 transformations that need to be taken into account in this problem. The -3 moves the function 3 units down. So the midline is now y=-3. The amplitude is 5. So from the midline, the graph will be 5 units up and down from there. That will be the range. From -3+5 = 2 and -3-5 = -8. So the range is [-8,2]

Note: The horizontal shift and reflection do not change the range.