f(x)= x+5, if x>0
3, if x¡Ü0
and how would i graph this?
To graph the given function f(x) = x + 5, if x > 0 and f(x) = 3, if x ≤ 0, you can follow these steps:
1. Firstly, locate the y-intercept. In this case, when x ≤ 0, f(x) is always equal to 3. So, plot a point at (0, 3).
2. Next, consider the behavior of f(x) when x > 0. As x increases, f(x) also increases, because f(x) = x + 5. This means that the graph should have a positive slope here.
3. To determine the slope of the function, choose any arbitrary value for x that is greater than 0. For example, let's take x = 1. By substituting this value into the equation f(x) = x + 5, we find f(1) = 1 + 5 = 6. So, plot the point (1, 6).
4. Now, draw a straight line from (0, 3) to (1, 6), representing the function for x > 0.
5. Finally, extend the line you just drew infinitely in both directions to show that the function continues in the same manner for all x > 0.
The completed graph will have a horizontal line at y = 3 for x ≤ 0 and a line with positive slope for x > 0.