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

Answer:

[-4,2] is the range

Step-by-step 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]