f(x)= x+5, if x>0
3, if x<=0
how do i graph and solve this function?
what number did they give you because you have to plug the answer in for X these are two differnt parts. The question is say use X+5 if x is greater than 0 or the answer is three if x is less than 0
To graph this function, you can follow these steps:
1. Plot the points where the function changes its behavior:
- At x = 0, the function changes from f(x) = 3 to f(x) = x + 5.
2. Draw a dotted line at x = 0 as a reminder of the change in behavior.
3. For x > 0: Starting from the point (0, 3), use a straight line with a slope of 1 to represent the function f(x) = x + 5. This means that for every increase in x by 1, the value of f(x) increases by 1.
- Plot a point at (1, 6). Since x = 1 and f(x) = x + 5, we have f(1) = 1 + 5 = 6.
- Plot another point at (2, 7), where f(2) = 2 + 5 = 7.
- Continue plotting points in a similar manner.
4. For x ≤ 0: Use a horizontal line at y = 3 to represent the function f(x) = 3.
- Plot a few points to verify: (0, 3), (-1, 3), (-2, 3), and so on.
5. Connect all the plotted points with straight lines to form the graph.
To solve the function, you can follow these steps:
- For x > 0: To find the value of y (f(x)) for a given x, simply substitute the value of x into the equation f(x) = x + 5. For example, if x = 2, then f(2) = 2 + 5 = 7.
- For x ≤ 0: The equation f(x) = 3 is constant for all x less than or equal to 0. So regardless of the value of x, f(x) will always be 3.
That's how you can graph and solve the function f(x) = x + 5, if x > 0, and f(x) = 3, if x ≤ 0.