Question

What function represents a translation of the logarithmic function f(x) = log2 x that is 4 units to the right and 8 units up?

a) f(x) = log2(x - 4) + 8
b) f(x) = log2(x + 4) + 8
c) f(x) = log2(x) + 4
d) f(x) = log2(x) + 8

Domain:
a) 4 < x < [infinity]
b) -4 < x < [infinity]
c) x > 0
d) x > 0

Range:
a) -[infinity] < y < [infinity]
b) -[infinity] < y < [infinity]
c) -[infinity] < y < [infinity]
d) -[infinity] < y < [infinity]

Answer 1

The translated function you are looking for is f(x) = log2(x - 4) + 8, with a domain of 4 < x < [infinity] and a range of -[infinity] < y < [infinity].

Step-by-step explanation:

To find the function that represents a translation of the logarithmic function f(x) = log2 x 4 units to the right and 8 units up, we need to shift the input of the function (x) to the left by 4 units and then add 8 to the result of the function. This is done by replacing x with (x - 4) and adding 8 to the whole function, resulting in f(x) = log2(x - 4) + 8.

The domain of the translated function will start 4 units to the right of the original function, so since the original domain for log2 x is x > 0, the new domain will be x > 4. This corresponds to option a) 4 < x < [infinity]. The range of a logarithmic function is always -[infinity] < y < [infinity], which is not affected by translations, so this remains the same and corresponds to option a), b), and c).