Final answer:
The statement is true; if f(x) has a relative max at x=8, it means f(x) is increasing as x approaches 8 and decreasing as x moves beyond 8, creating a peak at x=8 on the graph.
Step-by-step explanation:
If f(x) has a relative max when x=8, then the statement that f(x) is increasing as x increases toward 8 and is decreasing as x increases from 8 is true.
Here's why: when we talk about a function having a relative maximum at a certain point, we're indicating that f(x) reaches a peak at that point. For f(x) to have a relative maximum at x=8, it must increase as we approach x=8 from the left (that is, as x gets closer to 8, but is less than 8) and must decrease as we move away from x=8 on the right (that is, x is greater than 8). This creates a hill-like shape on the graph of f(x), where the top of the hill is the relative maximum at x=8.
If f(x) were instead a horizontal line, there would be no increase or decrease, and thus no maximum or minimum points; the function's value would be constant. However, this is not the case here since the function is described as having a relative maximum at x=8.