The reciprocal parent function then is translated 8 units left and 3 units up. write an equation to represent this function. then identify the asymptotes

Answer 1

The reciprocal function is f(x) = 1/x

To translate it 8 units left, group +8 with the x (note that you always group the opposite value with the x so moving left is a positive 8. That becomes f(x) = 1/(x+8)

Then to move it up by 3 units, just add 3:

f(x) = 1/(x+8) + 3

The vertical asymptote is when the denominator equals zero (x = -8), The horizontal asymptote is at y = 3 since 1/(x+8) can never equal zero, 1/(x+8) + 3 can never equal 3