Question
y=3sin(2x+1)-2 vertical and horizontal stretch
Answers
GPT 3.5
To find the vertical and horizontal stretches of the function y = 3sin(2x+1) - 2, we first need to compare it to a standard form of the sine function, y = sin(x).
The general form of the sine function is y = a*sin(bx+c) + d, where:
a is the vertical stretch factor
b is the horizontal stretch factor
c is the horizontal shift
d is the vertical shift
In our given function y = 3sin(2x+1) - 2, the a value is 3 and the b value is 2.
Vertical Stretch Factor (a): The vertical stretch factor magnifies or shrinks the graph vertically. The vertical stretch factor in this case is 3, which means the graph is stretched vertically by a factor of 3.
Horizontal Stretch Factor (b): The horizontal stretch factor compresses or stretches the graph horizontally. The horizontal stretch factor in this case is 2, which means the graph is stretched horizontally by a factor of 1/2.
Therefore, the given function has a vertical stretch factor of 3 and a horizontal stretch factor of 1/2.
The general form of the sine function is y = a*sin(bx+c) + d, where:
a is the vertical stretch factor
b is the horizontal stretch factor
c is the horizontal shift
d is the vertical shift
In our given function y = 3sin(2x+1) - 2, the a value is 3 and the b value is 2.
Vertical Stretch Factor (a): The vertical stretch factor magnifies or shrinks the graph vertically. The vertical stretch factor in this case is 3, which means the graph is stretched vertically by a factor of 3.
Horizontal Stretch Factor (b): The horizontal stretch factor compresses or stretches the graph horizontally. The horizontal stretch factor in this case is 2, which means the graph is stretched horizontally by a factor of 1/2.
Therefore, the given function has a vertical stretch factor of 3 and a horizontal stretch factor of 1/2.