how do i find the rule of a piecewise linear function?
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Piecewise linear function
Find the next three terms in the arithmetic sequence.
-10, -7, -4, -1, . . .
To find the rule of a piecewise linear function, you need to determine the equations of the individual linear segments that make up the function.
Here's a step-by-step process to find the rule of a piecewise linear function:
1. Identify the different segments: Look at the graph and identify the distinct segments or intervals that make up the function. Each segment represents a different equation.
2. Determine the slope for each segment: Examine each segment and find the slope. The slope of a linear function is given by the formula:
slope = (change in y) / (change in x)
Find two points on each segment and calculate the change in y and change in x to determine the slope.
3. Find the y-intercept for each segment: Using the equation of a straight line, y = mx + b, where m is the slope and b is the y-intercept, you need to find the y-intercept (b) for each segment. For this, pick any point on the segment and substitute the x and y values into the equation to solve for b.
4. Write the equation for each segment: Now that you have the slope and the y-intercept for each segment, you can write the equation of each segment. Use the formula y = mx + b, with the previously calculated values.
5. Combine the equations for all segments: Write the equation for each segment in a piecewise function notation. For example:
f(x) = { equation1 if x < a,
equation2 if a ≤ x < b,
equation3 if b ≤ x < c,
...
equationn if x ≥ z}
Replace "equation1", "equation2", etc., with the equations obtained for each segment, and "a", "b", etc., with the respective x-values where the segments intersect.
Following these steps will help you find the rule of a piecewise linear function.