Answer:
[tex]\boxed{\boxed{\pink{\bf \leadsto The \ range \ of \ y \ is \ y \ \in \ [-5,5] .}}}[/tex]
Step-by-step explanation:
A function is given to us and we need to find its range. So the given function is ,
[tex]\bf\implies y = -5\:sin(x) [/tex]
The lower bound of the range for sine is found by substituting the negative magnitude of the coefficient into the equation.
[tex]\bf \implies y = (-5) [/tex]
The upper bound of the range for sine is found by substituting the positive magnitude of the coefficient into the equation.
[tex]\bf \implies y = (5) [/tex]
Hence the range is ,
[tex]\boxed{\red{\bf -5 \leq y \leq 5 }}[/tex]
Interval Notation :-
[tex]\boxed{\red{\bf y \in [-5,5] }}[/tex]
Set builder Notation :-
[tex]\boxed{\red{\bf \{ y | -5 \leq y \leq 5 }}[/tex]
Graph of the function is attached .
Hence the range of y = -5 sin(x) is [-5,5].
