Question

The function g is defined by g(x) = 3 sin ( 2x + 1 ) - 1 what is the range of g?

how can i know?

Answer 1

[-4,2] is the range

Explanation:

A parent function of sine is known to have range of -A ≤ y ≤ A where A stands for amplitude.

Therefore, we would have the range:

`\displaystyle{ - 3 \leqslant g(x) \leqslant 3}`

But since there's a vertical shift of -1, we have to subtract -1 from both -3 and 3.

`\displaystyle{ - 4 \leqslant g(x) \leqslant 2}`

Therefore, the range of function is [-4,2]