Apply a reflection and translation down 3 units to the following
G(x)=3x-2
To apply a reflection and translation to the function G(x)=3x-2, we need to follow these steps:
Step 1: Reflection
To reflect the function, we can use the negative sign (-) in front of the function. This will reflect the graph across the x-axis. So the reflected function, let's call it H(x), will be:
H(x) = -G(x)
Step 2: Translation
To translate the function downward by 3 units, we need to subtract 3 from the function. So the translated and reflected function, let's call it F(x), will be:
F(x) = H(x) - 3
Putting it all together:
1. Reflect the function: H(x) = -G(x) = -3x + 2.
2. Translate the reflected function downward: F(x) = H(x) - 3 = (-3x + 2) - 3 = -3x - 1.
Therefore, the final function after applying the reflection and translation is F(x) = -3x - 1.