- Introduction to piecewise functions
- Worked example: evaluating piecewise functions
- Evaluate piecewise functions
- Evaluate step functions
- Worked example: graphing piecewise functions
- Piecewise functions graphs
- Worked example: domain & range of step function
- Worked example: domain & range of piecewise linear functions
- Absolute value & piecewise functions: FAQ
Absolute value & piecewise functions: FAQ
Frequently asked questions about absolute value & piecewise functions
What is absolute value?
Absolute value is a function that outputs the distance of any input from on the number line. We often write the absolute value of a number with vertical bars on either side, like .
What do graphs of absolute value functions look like?
For the most basic absolute value function, , the graph looks like a "V" shape with the vertex at the origin. As we modify the function (for example, by shifting it vertically or horizontally), the graph will change accordingly, but it will maintain the general "V" shape.
Practice with our Shift absolute value graphs exercise.
Practice with our Scale & reflect absolute value graphs exercise.
Practice with our Graph absolute value functions exercise.
What are piecewise functions?
Piecewise functions are functions that are defined in separate "pieces" for different intervals of the input. For example, we could define a piecewise function like this:
This function will multiply an input by for inputs less than or equal to , and multiply it by and add for inputs greater than .
Practice with our Evaluate piecewise functions exercise.
What do graphs of piecewise functions look like?
The graph of a piecewise function will depend on the specific function itself. However, a common feature is that the graph may appear "broken" or disjointed at the points where the function changes definitions. For the function above, the graph will be two different lines that meet at the origin.
Practice with our Piecewise functions graphs exercise.
Where are absolute value functions and piecewise functions used in the real world?
Both types of functions are used in a variety of contexts. Absolute value functions can be helpful when we want to measure distances or find the magnitude of a certain quantity. Piecewise functions are often used to model situations where different rules or formulas apply in different situations.
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- you are totally right, I never thought about it like this before!!(4 votes)
- In piecewise functions such as f(x)= 1. 5, x=7
2. 8, x=3
3. 6x-4, x is not 7 or 3
does the graph shape in a way where the graph 6x-4 is drawn but has holes in y values where x is 7 or 3, and for 7 and 3, there are points for (7,5) and (3,8)?(2 votes)
- No, the graph's shape will not change from a line. There will be holes where x equals 7 and 3, and the 2 points, (7,5) and (8,3), are plotted separately.(2 votes)