Final answer:
The functions f(0) = f(x-1)-2, h(x) = 3/2(4x), g(n) = 3/2(n) - 4, and t(n)= (n-1)-1 are all linear functions, except f which relates to recursive or shifted functions. h(x) and g(n) have specific slopes of 6 and 3/2 respectively, while t(n) is simplified to a straight line with a slope of 1.
Step-by-step explanation:
To classify each function with its description, we need to examine the structure and properties of the given functions.
f(0) = f(x-1)-2
This function suggests that the output of f at x is related to the output of f at x-1, but decreased by 2. This implies a translation and decrease in value, which can occur in recursive functions or functions that relate their output to prior inputs after some modification.
h(x) = 3/2(4x)
The function h(x) is a linear function with a slope of 6 (since 3/2 times 4 is 6) which means it increases linearly as x increases.
g(n) = 3/2(n) - 4
g(n) is also a linear function with a slope of 3/2 and a y-intercept of -4. This function represents a straight line on a graph with these characteristics.
t(n)= (n-1)-1
The function t(n) is another linear function that can be simplified to t(n) = n - 2. This means it has a slope of 1 and a y-intercept of -2. It is a straight line with these traits.