Question

F(x)=x+2

f(x) is positive when (-2, infinity) and negative when (-infinity, -2). What does this mean and how is this shown on the graph? Please explain.

Answer 1

To determine when a function is positive or negative on a certain interval, we can analyze the sign of the function. In this case, the function f(x) = x + 2f(x) is negative when x < -2 and positive when x > -2. This can be represented on a graph by drawing a horizontal line at y = -2 and indicating the positive and negative regions.

Step-by-step explanation:

To understand what it means for a function to be positive or negative on a specific interval, we need to analyze the sign of the function. In this case, we have the function f(x) = x + 2f(x). To find when this function is positive and negative, we need to solve for x.

Let's start by rearranging the equation to isolate f(x). We have:

f(x) = x + 2f(x) -> f(x) - 2f(x) = x -> -f(x) = x -> f(x) = -x

Now we can analyze the sign of f(x) on the given intervals. When x is greater than -2, f(x) will be negative because it is equal to -x. When x is less than -2, f(x) will be positive. This is why f(x) is negative on the interval (-∞, -2) and positive on the interval (-2, ∞).

On a graph, this can be shown by drawing a horizontal line at the y-value of -2 and indicating that f(x) is negative below that line, and positive above that line.