What are the vertical and horizontal stretch/compressions for the functions h(x)=1/(5x) and k(x)=|0.4x| ?
To determine the vertical and horizontal stretch/compressions for the given functions, let's analyze each function separately.
1. For the function h(x) = 1/(5x):
Vertical Stretch/Compression:
The vertical stretch or compression is determined by the coefficient in front of the function. In this case, the coefficient is 1/5. A coefficient greater than 1 indicates a vertical compression, while a coefficient between 0 and 1 indicates a vertical stretch. Therefore, the function h(x) has a vertical stretch of 5.
Horizontal Stretch/Compression:
The horizontal stretch or compression is determined by the coefficient inside the function. In this case, the coefficient is 5x. To find the horizontal stretch or compression, we take the reciprocal of the coefficient. So, the horizontal stretch or compression for h(x) is 1/5.
In summary, the function h(x) = 1/(5x) has a vertical stretch of 5 and a horizontal compression of 1/5.
2. For the function k(x) = |0.4x|:
Vertical Stretch/Compression:
The absolute value function does not have a vertical stretch or compression since it retains the same shape regardless of the coefficient or constant.
Horizontal Stretch/Compression:
The coefficient inside the absolute value function determines the horizontal stretch or compression. In this case, the coefficient is 0.4x. To find the horizontal stretch or compression, we take the reciprocal of the coefficient. So, the horizontal stretch or compression for k(x) is 1/0.4, which simplifies to 2.5.
In summary, the function k(x) = |0.4x| does not have a vertical stretch or compression and has a horizontal compression of 2.5.