Explain how the transformations of the functions f(x)=15sin(x) and f(x)=sin(x)+15 differ.
I see that f(x)=sin(x)+15 experiences a vertical shift, but I am not sure about the transformation that f(x)=15sin(x) experiences. Thank you for your help!
compared to f(x) = sinx
15 sinx has its amplitude changed from 1 to 15
sinx + 15 simply shifts sinx up 15 units.
You had the last one correct
see the graphs here:
http://www.wolframalpha.com/input/?i=plot+y+%3D+sinx+%2C+y+%3D+15sinx+%2C+y+%3D+sinx+%2B+15
Thank you!
Sure! To understand the differences in transformations between the functions f(x) = 15sin(x) and f(x) = sin(x) + 15, let's break down each function separately.
1. f(x) = 15sin(x):
The function f(x) = 15sin(x) involves the standard sine function sin(x), which oscillates between -1 and +1. Multiplying sin(x) by 15 stretches the amplitude of the sine function by a factor of 15. This means that the peaks and troughs of the graph will be stretched 15 units vertically.
2. f(x) = sin(x) + 15:
On the other hand, the function f(x) = sin(x) + 15 adds a constant 15 to the sine function sin(x). This constant vertical shift adds 15 units to the graph of sin(x) at every point. The shape of the graph remains the same, but the entire graph is shifted upwards by 15 units.
To summarize:
- f(x) = 15sin(x) stretches the graph vertically by a factor of 15.
- f(x) = sin(x) + 15 shifts the graph vertically by 15 units upwards.
Remember, if you're not sure about the transformations, you can plot the graphs using a graphing calculator or software to visually see the differences.