Question

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?

a) ƒ(x) = 6x − 7 − 3

b) ƒ(x) = 6x − 3 − 7

c) ƒ(x) = 6x + 7 − 3

d) ƒ(x) = 6x − 3 + 7

Answer 1

The function f(x) after being translated down by 3 units and right by 7 units from g(x) = 6^x is f(x) = 6^(x - 7) - 3.

Step-by-step explanation:

To find the function f(x), we need to apply the translations to the original function g(x) = 6x. Translating a function down by 3 units will subtract 3 from the function, while translating it right by 7 units means we replace every x in the function with (x - 7). Therefore, the new function after translation will be f(x) = 6(x - 7) - 3.