Final answer:
The value of k in the function f(x) is determined to be -5 by using the Remainder Theorem and substituting the given values into the function.
Step-by-step explanation:
The value of k in the function f(x) = 3x^2 - 4x + k can be found by using the Remainder Theorem which states that the remainder of a polynomial f(x) when divided by (x - a) is f(a). Here, we are given that the remainder is 79 when f(x) is divided by (x - 6), so we substitute 6 for x in the given function to find the remainder:
f(6) = 3(6)^2 - 4(6) + k = 108 - 24 + k = 84 + k
Since the remainder is 79, we set up the following equation:
84 + k = 79
Now subtract 84 from both sides to find the value of k:
k = 79 - 84
k = -5
Therefore, the value of k is -5.