which set of transformations is needed to graph (f(x)= -2sin(x)+3) from the parent sine function?\nvertical…

which set of transformations is needed to graph (f(x)= -2sin(x)+3) from the parent sine function?\nvertical compression by a factor of 2, vertical translation 3 units up, reflection across the y - axis\nvertical compression by a factor of 2, vertical translation 3 units down, reflection across the x - axis\nreflection across the x - axis, vertical stretching by a factor of 2, vertical translation 3 units up\nreflection across the y - axis, vertical stretching by a factor of 2, vertical translation 3 units down

which set of transformations is needed to graph (f(x)= -2sin(x)+3) from the parent sine function?\nvertical compression by a factor of 2, vertical translation 3 units up, reflection across the y - axis\nvertical compression by a factor of 2, vertical translation 3 units down, reflection across the x - axis\nreflection across the x - axis, vertical stretching by a factor of 2, vertical translation 3 units up\nreflection across the y - axis, vertical stretching by a factor of 2, vertical translation 3 units down

Answer

Answer:

Reflection across the x - axis, vertical stretching by a factor of 2, vertical translation 3 units up

Explanation:

Step1: Analyze the coefficient of sin(x)

The negative sign in front of 2sin(x) reflects the parent function y = sin(x) across the x - axis.

Step2: Analyze the multiplier of sin(x)

The coefficient 2 in - 2sin(x) vertically stretches the function by a factor of 2.

Step3: Analyze the constant term

The + 3 in - 2sin(x)+3 vertically translates the function 3 units up.