The function ƒ(x) is a translation of the exponential function g(x) = 6x. What's ƒ(x) if the translation is down 3 units and right 7 units?

f(x) = 6ˣ⁻⁷-3

Step-by-step explanation:

The basic transformations of an exponential function from the parent function can be given by the equation:

f(x) = b^x [parent exponential function]

f(x) = ab^((x/c)-h) + k [transformation of parent exponential function]

Where b is the parent growth or decay, a is the vertical stretch or compression, c is the horizontal stretch or compression, h is the horizontal translation, and k is the vertical translation.

Given a translation down 3 units, and another translation right 7 units, we are only using h, and k.

Given that our original function is g(x) = 6ˣ. We know our parental growth or b is 6. So just substitute our quantities and solve:

f(x) = g(x-7) - 3 → (1)6^((x/1)-7) - 3 → 6^(x-7) - 3 → 6ˣ⁻⁷-3.