Final answer:
To determine if the function is positive or negative over a given interval, one would typically assess its graph or algebraic expression. A positive slope means the function rises as x increases, a negative slope means it falls, and a zero slope means it is constant. Without the specific function, we cannot definitively say if it is positive or negative in the interval -5 < x < 4.
Step-by-step explanation:
To determine whether the function is positive or negative over the interval -5 < x < 4, we would need the specific function equation, which is not provided. However, I can explain how the appearance of positive slope, negative slope, and zero slope differ on a graph which might help in understanding the behavior of a function.
- A positive slope means that as the x-value increases, the y-value also increases. Graphically, this is represented by a line that rises as it moves from left to right.
- A negative slope has the opposite behavior; as the x-value increases, the y-value decreases. On a graph, a negative slope is represented by a line that falls as it moves from left to right.
- A zero slope indicates that there is no change in the y-value as the x-value increases. This is represented by a horizontal line on the graph.
For example, if a graph has a y-intercept of 50 and a positive slope, it will gradually rise as the x-value increases. For a function represented by a horizontal line, such as f(x) = 20 (over the interval 0 ≤ x ≤ 20), the slope would be zero, meaning there is no rise and therefore the function value does not change—it stays positive at 20 across the interval.