reflected over the x-axis then translated 5 units left

Answer 1

f(x) reflected over the x axis makes (x,y) = (x,-y)

translated 5 units left means replace x with x+5

for example, if f(x) = x^2,

then g(x) = -x^2 with a reflection over the x axis,

then h(x) = -(x+5)^2 when translated 5 units left

for example if f(x) = y = x

with translation 5 units left, then y=x+5

the "to the left" suggests a negative change, but change x to x+5, not to x-5. what used to be point (0,0) on the line y=x becomes the point (-5,0) on the translated line to the left, but the equation of the new translated line is y=x+5

Answer 2

Start with the translation that is given first, for example the reflection over the x-axis.

(x, y) ----> (x, -y)

Then translate five units to the left (meaning the coordinate is going backwards essentially), meaning that this set of instructions affects the x-axis only, so:

(x - 5, -y)

I hope that is helpful!