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.