Given the one point function (3,9) (in other words f(3)=9) Identify the following transformations
f(2x)
-3(f(x-4))+1
f(5x+3)
4f(-x)
To identify the transformations for each function, we need to understand how each operation affects the original function. Let's break it down step by step:
1. f(2x):
This transformation takes the original function and applies a horizontal compression by a factor of 1/2. It means that the function will be stretched horizontally, making it twice as steep. In simpler terms, the x-values of the original function will be divided by 2.
2. -3(f(x-4))+1:
Here we have a few transformations in play:
- The original function is shifted horizontally 4 units to the right.
- The function is then multiplied by -3, reflecting it about the x-axis. This will flip the sign of the y-values, making it an upside-down graph.
- Lastly, the reflected function is shifted vertically 1 unit up.
3. f(5x+3):
This transformation involves the following steps:
- The original function is compressed horizontally by a factor of 1/5, meaning that the x-values are divided by 5.
- The function is then shifted horizontally to the left by 3 units.
4. 4f(-x):
In this case, we have the following transformations:
- The original function is reflected about the y-axis by multiplying the x-values by -1.
- The reflected function is then multiplied by 4, which affects the y-values and stretches the graph vertically.
By applying these transformations to the original point (3,9), you can determine the transformed coordinates for each function accordingly.