How can I tell whether a function will be reflected in the x-axis or y-axis and whether it will be horizontally and vertically compressed or not?
For example, this function:
y=-2f(4(x-2)) + 8
Wouldn't it depend what f(z) was? For instance, if f(z)=z^2, then
f(4(x-2)) would be 16(x-2)^2 which would reflect about x=2
Oh, sorry I wasn't clear.
I didn't mention that it's supposed to be graphed from y = f(x). Also, we just write out how to obtain the graph, not the exact coordinates.
So I think from
y=-2f(4(x-2)) + 8
-Vertically stretched by a factor of 2, and horizontally stretched by a factor of 1/4
-Reflected in the x-axis
-Translated 2 units right, 8 units up
Is this correct?
To determine the reflection and compression of a function, you need to analyze the roles of the coefficients and constants in the function equation.
In the given function: y = -2f(4(x - 2)) + 8
1. Reflection:
The reflection occurs based on the sign of the coefficient in front of the function, which is -2 in this case.
- If the coefficient is positive, the function is not reflected.
- If the coefficient is negative, the function is reflected across the x-axis.
In this example, since the coefficient is -2, the function is reflected across the x-axis.
2. Horizontal Compression/Expansion:
The horizontal compression/expansion occurs based on the value inside the function, which is 4 in this case.
- If the value inside the function is greater than 1, the function is horizontally compressed.
- If the value inside the function is less than 1, the function is horizontally expanded.
- If the absolute value of the value inside the function is greater than 1, the compression/expansion is more significant.
In this example, since the value inside the function is 4, the function is horizontally compressed.
3. Vertical Compression/Expansion:
The vertical compression/expansion occurs based on the value outside the function or the constant, which is -2 in this case.
- If the coefficient or constant outside the function is greater than 1, the function is vertically compressed.
- If the coefficient or constant outside the function is less than 1, the function is vertically expanded.
- If the absolute value of the coefficient or constant outside the function is greater than 1, the compression/expansion is more significant.
In this example, since the constant outside the function is -2, the function is vertically compressed.
By analyzing these factors, we can determine that the given function is reflected across the x-axis, horizontally compressed, and vertically compressed.