how do you graph f(x)={2x+5 if x<0
{5 if 0¡Üx¡Ü10
{2x-10 if x>10
(the {'s is supposed to be one long one)
To graph the function f(x) = {2x + 5 if x < 0, 5 if 0 ≤ x ≤ 10, 2x - 10 if x > 10, we will divide it into three separate cases and graph each part individually. Here's how you do it step by step:
Case 1: x < 0
For x < 0, the function is defined as f(x) = 2x + 5.
To graph this part, you can choose several x-values below 0 and compute the corresponding y-values using the equation. For example, if we choose x = -2, then y = 2(-2) + 5 = 1.
You can repeat this process for other x-values, and then plot the points (x, y) on the graph. It's important to connect these points with a straight line since it is a linear function.
Case 2: 0 ≤ x ≤ 10
For 0 ≤ x ≤ 10, the function is defined as f(x) = 5.
Since this part is a constant function, the y-value remains the same (5) for all x-values between 0 and 10. Therefore, you can simply draw a horizontal line at y = 5 within this range.
Case 3: x > 10
For x > 10, the function is defined as f(x) = 2x - 10.
Similar to Case 1, you need to choose several x-values greater than 10 and calculate the corresponding y-values. For example, if we choose x = 12, then y = 2(12) - 10 = 14.
Again, plot these points on the graph and connect them with a straight line.
Combining all three cases, you will have a piecewise graph that represents the function f(x).
Note: Make sure to label the x and y-axes appropriately, indicating the scale units and the intervals along each axis.