Apply a reflection and translation down 3 units to the following:
G(x)=3x-2
what kind of reflection ?
Reflection is when the sign of slope changes but I need a translation too!!
When the slope of the line changes its sign, that would be a reflection in the y-axis
There are many different kinds of reflections, the above is just one of them
so y = 3x - 2 ----> y = -3x - 2 , a reflection in the y-axis
now down 3
y = -3x-2 - 3
or
y = -3x - 5
To apply a reflection and translation to the function G(x) = 3x - 2, you'll follow these steps:
Step 1: Apply the reflection.
To reflect the function, you need to multiply the function by -1. This will flip the function over the x-axis. The reflection of G(x) = 3x - 2 would be -G(x) = -3x + 2.
Step 2: Apply the translation.
To translate the function downward by 3 units, you need to subtract 3 from the function. The translated function would be -G(x) - 3 = -3x + 2 - 3.
Simplifying the equation further, you get -G(x) - 3 = -3x - 1.
Therefore, by applying a reflection and translation down 3 units to G(x) = 3x - 2, the transformed equation would be -G(x) - 3 = -3x - 1.