how to graph f(x)={3x+2 if x<5
{-3x-2 if x¡Ý5
(the {'s are supposed to be one long one)
To graph the function f(x) with the given piecewise definition, follow these steps:
Step 1: Identify the domain of the function
In this case, the domain consists of all real numbers since there are no restrictions mentioned.
Step 2: Determine the behavior of f(x) for different intervals
Since the function has two different expressions based on the value of x, we need to consider two cases: x < 5 and x ≥ 5.
Case 1: x < 5
For x < 5, the function is defined as f(x) = 3x + 2.
To graph this line segment, you can start by choosing a few x-values smaller than 5 and calculate the corresponding y-values using the equation f(x) = 3x + 2. Plot these points on the coordinate plane and then connect them to form a straight line.
Case 2: x ≥ 5
For x ≥ 5, the function is defined as f(x) = -3x - 2.
Similarly, choose a few x-values greater than or equal to 5 and calculate the corresponding y-values. Plot these points on the graph and connect them to form another straight line.
Step 3: Combine the two line segments
Once you have graphed both line segments, you should have two distinct lines. Since the function changes its expression at x = 5, draw an open circle (○) at the point (5, f(5)) to indicate that it is not included in the graph. This is because the function has different values just before and after x = 5.
Step 4: Add labels and scale
Finally, label the x and y axes and add any other necessary descriptions for the graph. Also, scale the graph appropriately to ensure all the relevant points are plotted within the visible area.
Remember to follow these steps carefully, and you will be able to graph the function f(x) with the given piecewise definition.